Showing papers on "Stochastic process published in 2013"
TL;DR: Two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems.
Abstract: In this paper, the problem of sampled-data synchronization for Markovian jump neural networks with time-varying delay and variable samplings is considered. In the framework of the input delay approach and the linear matrix inequality technique, two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems. The desired mode-independent controller is designed, which depends upon the maximum sampling interval. The effectiveness and potential of the obtained results is verified by two simulation examples.
567 citations
TL;DR: This paper proposes to analyze downlink performance in a fixed-size cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers, using recent applications of stochastic geometry to analyze cellular systems.
Abstract: Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated, making evaluation of different communication strategies challenging in both analysis and simulation. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper proposes to analyze downlink performance in a fixed-size cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers. A nearest out-of-cell interferer, out-of-cell interferers outside a guard region, and cross-tier interferers are included in the interference calculations. Bounding the interference power as a function of distance from the cell center, the total interference is characterized through its Laplace transform. An equivalent marked process is proposed for the out-of-cell interference under additional assumptions. To facilitate simplified calculations, the interference distribution is approximated using the Gamma distribution with second order moment matching. The Gamma approximation simplifies calculation of the success probability and average rate, incorporates small-scale and large-scale fading, and works with co-tier and cross-tier interference. Simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge.
451 citations
TL;DR: A novel metric, the deployment gain, is introduced and it is demonstrated how it can be used to estimate the coverage performance and average rate achieved by a data set.
Abstract: The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. In this paper, different spatial stochastic models (the Poisson point process (PPP), the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice) are used to model the structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting. One is fitting by the method of maximum pseudolikelihood. As for the fitted models, it is not sufficient to distinguish them conclusively by some classical statistics. We propose the coverage probability as the criterion for the goodness-of-fit. In terms of coverage, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately. Furthermore, we introduce a novel metric, the deployment gain, and we demonstrate how it can be used to estimate the coverage performance and average rate achieved by a data set.
308 citations
TL;DR: An analytical framework to compute the average rate of downlink heterogeneous cellular networks is introduced, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal.
Abstract: In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.
300 citations
TL;DR: In this paper, a variational principle based on the maximization of a Rayleigh coefficient is derived for modeling the slow parts of Markov processes by approximating the dominant eigenfunctions and eigenvalues of the propagator.
Abstract: The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due to the sampling problems. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the dominant eigenfunctions and eigenvalues of the propagator. To this end, a variational principle is derived that is based on the maximization of a Rayleigh coefficient. It is shown that this Rayleigh coefficient can be estimated from statistical observables that can be obtained from short distributed simulations starting from different parts of state space. The approach forms a basis for the development of adaptive and efficient computational algorithms for simulating and analyzing metastable Markov processes while avoiding the sampling problem. Since any stochastic process with finite memory can be transformed into a Markov process, the approach is applicable to a wide range of processes relevant for modeling complex real-world phenomena.
281 citations
TL;DR: In this paper, a finite difference algorithm is proposed to compute the motion of an optically trapped particle and the numerical treatment of the white noise term, and the transition from the ballistic to the diffusive regime due to the presence of inertial effects on short time scales is examined.
Abstract: An optically trapped Brownian particle is a sensitive probe of molecular and nanoscopic forces. An understanding of its motion, which is caused by the interplay of random and deterministic contributions, can lead to greater physical insight into the behavior of stochastic phenomena. The modeling of realistic stochastic processes typically requires advanced mathematical tools. We discuss a finite difference algorithm to compute the motion of an optically trapped particle and the numerical treatment of the white noise term. We then treat the transition from the ballistic to the diffusive regime due to the presence of inertial effects on short time scales and examine the effect of an optical trap on the motion of the particle. We also outline how to use simulations of optically trapped Brownian particles to gain understanding of nanoscale force and torque measurements, and of more complex phenomena, such as Kramers transitions, stochastic resonant damping, and stochastic resonance.
231 citations
TL;DR: The first attempt to characterize the uncertainties entering into the inner coupling matrix is made with the aid of the interval matrix approach, and a novel measurement model is proposed to account for these phenomena occurring with individual probability.
Abstract: In this paper, the H∞ state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements. With the aid of the interval matrix approach, we make the first attempt to characterize the uncertainties entering into the inner coupling matrix. The incomplete measurements under consideration include sensor saturations, quantization, and missing measurements, all of which are assumed to occur randomly. By introducing a stochastic Kronecker delta function, these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability. With the measurement model, a set of H∞ state estimators is designed such that, for all admissible incomplete measurements as well as the uncertain coupling strength, the estimation error dynamics is exponentially mean-square stable and the H∞ performance requirement is satisfied. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method. Finally, a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.
222 citations
TL;DR: It is shown that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power.
Abstract: The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.
215 citations
TL;DR: The proposed RDE approach is shown to be suitable for online application without the need of increasing the problem size and the effectiveness of the proposed method is demonstrated in the numerical example.
Abstract: In this paper, a new H∞ filtering approach is developed for a class of discrete time-varying systems subject to missing measurements and quantization effects. The missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval [0,1] . The measured output is quantized by a logarithmic quantizer. Attention is focused on the design of a stochastic H∞ filter such that the H∞ estimation performance is guaranteed over a given finite-horizon in the simultaneous presence of probabilistic missing measurements, quantization effects as well as external non-Gaussian disturbances. A necessary and sufficient condition is first established for the existence of the desired time-varying filters in virtue of the solvability of certain coupled recursive Riccati difference equations (RDEs). Owing to its recursive nature, the proposed RDE approach is shown to be suitable for online application without the need of increasing the problem size. The simulation experiment is carried out for the mobile robot localization problem with non-Gaussian disturbances, missing measurements and quantization effects. The effectiveness of the proposed method is demonstrated in the numerical example.
213 citations
TL;DR: In this paper, the existence of mild solutions for a class of fractional stochastic differential equations with impulses in Hilbert spaces was studied and sufficient conditions for mild solutions were formulated and proved.
Abstract: The fractional stochastic differential equations have wide applications in various fields of science and engineering. This paper addresses the issue of existence of mild solutions for a class of fractional stochastic differential equations with impulses in Hilbert spaces. Using fractional calculations, fixed point technique, stochastic analysis theory and methods adopted directly from deterministic fractional equations, new set of sufficient conditions are formulated and proved for the existence of mild solutions for the fractional impulsive stochastic differential equation with infinite delay. Further, we study the existence of solutions for fractional stochastic semilinear differential equations with nonlocal conditions. Examples are provided to illustrate the obtained theory.
TL;DR: In this article, a functional central limit theorem was proved for multivariate Hawkes processes observed over a time interval [ 0, T ] when T?? is a discrete scheme with mesh? over [ 0, T ] up to some further time shift.
TL;DR: By designing a novel Lyapunov functional, using some inequalities and the properties of random variables, several delay-dependent synchronization criteria are derived for the coupled networks of continuous-time version and its discrete-time analogues.
Abstract: This paper studies synchronization in an array of coupled neural networks with Markovian jumping and random coupling strength. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable and each node has an interval time-varying delay. By designing a novel Lyapunov functional, using some inequalities and the properties of random variables, several delay-dependent synchronization criteria are derived for the coupled networks of continuous-time version. Discrete-time analogues of the continuous-time networks are also formulated and studied. Some new lemmas are developed to obtain less conservative synchronization criteria of both continuous-time model and its discrete-time analogues. Numerical examples of both continuous-time system and its discrete-time analogues are finally given to demonstrate the effectiveness of the theoretical results.
TL;DR: A more accurate method that relaxes the assumption that upcrossings are independent by using joint upcrossing rates is developed and applied to the reliability analysis of a beam and a mechanism, and the results demonstrate a significant improvement in accuracy.
Abstract: In time-dependent reliability analysis, an upcrossing is defined as the event when a limit-state function reaches its failure region from its safe region. Upcrossings are commonly assumed to be independent. The assumption may not be valid for some applications and may result in large errors. In this work, we develop a more accurate method that relaxes the assumption by using joint upcrossing rates. The method extends the existing joint upcrossing rate method to general limit-state functions with both random variables and stochastic processes. The First Order Reliability Method (FORM) is employed to derive the single upcrossing rate and joint upcrossing rate. With both rates, the probability density of the first time to failure can be solved numerically. Then the probability density leads to an easy evaluation of the time-dependent probability of failure. The proposed method is applied to the reliability analysis of a beam and a mechanism, and the results demonstrate a significant improvement in accuracy.
TL;DR: The purpose of the addressed filtering problem is to design an unbiased and recursive filter for the random parameter matrices, stochastic nonlinearity, and multiple fading measurements as well as correlated noises.
TL;DR: A Bell test is provided that uses arbitrarily imperfect random bits to produce bits that are, under the non-signalling principle assumption, perfectly random, and provides the first protocol attaining full randomness amplification.
Abstract: Do completely unpredictable events exist? Classical physics excludes fundamental randomness. Although quantum theory makes probabilistic predictions, this does not imply that nature is random, as randomness should be certified without relying on the complete structure of the theory being used. Bell tests approach the question from this perspective. However, they require prior perfect randomness, falling into a circular reasoning. A Bell test that generates perfect random bits from bits possessing high-but less than perfect-randomness has recently been obtained. Yet, the main question remained open: does any initial randomness suffice to certify perfect randomness? Here we show that this is indeed the case. We provide a Bell test that uses arbitrarily imperfect random bits to produce bits that are, under the non-signalling principle assumption, perfectly random. This provides the first protocol attaining full randomness amplification. Our results have strong implications onto the debate of whether there exist events that are fully random.
TL;DR: The results presented depend on some easily-verified assumptions that are as elegant as those in the deterministic case, and the proofs themselves provide design procedures for switching controls.
Abstract: In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Ito's formula and Dynkin's formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-solution to the underlying problem is constructed and the boundedness criterion is proposed. The significance of this paper is that all the results presented depend on some easily-verified assumptions that are as elegant as those in the deterministic case, and the proofs themselves provide design procedures for switching controls.
TL;DR: In this paper, the photon correlation properties of different optical fields, including non-classical fields presenting an apparent violation of the Cauchy-Schwarz inequality, are discussed in a simple way through an analysis of the measurement scheme.
Abstract: Some general properties of photon correlations are discussed in a simple way through an analysis of the two-detector measurement scheme It is shown that the assumption of the discreteness of the random process leads directly to the conclusion that the zero-delay value of the correlation function is only bound to be non-negative The adopted approach allows discussing in a more intuitive way the photon correlation properties of different optical fields, including non-classical fields presenting an apparent violation of the Cauchy-Schwarz inequality The comparison between the two- and the single-detector experiment clarifies the role of the operator ordering in the definition of the correlation function
TL;DR: A novel adaptive and sequential gridding algorithm is presented and is expected to conform to the underlying dynamics of the model and thus to mitigate the curse of dimensionality unavoidably related to the partitioning procedure.
Abstract: This work is concerned with the generation of finite abstractions of general state-space processes to be employed in the formal verification of probabilistic properties by means of automatic techniques such as probabilistic model checkers. The work employs an abstraction procedure based on the partitioning of the state-space, which generates a Markov chain as an approximation of the original process. A novel adaptive and sequential gridding algorithm is presented and is expected to conform to the underlying dynamics of the model and thus to mitigate the curse of dimensionality unavoidably related to the partitioning procedure. The results are also extended to the general modeling framework known as stochastic hybrid systems. While the technique is applicable to a wide arena of probabilistic properties, with focus on the study of a particular specification (probabilistic safety, or invariance, over a finite horizon), the proposed adaptive algorithm is first benchmarked against a uniform gridding approach t...
TL;DR: In this article, a cooperative network with multiple source-destination pairs and one EH relay is considered and the outage probability experienced by users in this network is characterized by taking the spatial randomness of user locations into consideration.
Abstract: This letter considers a cooperative network with multiple source-destination pairs and one energy harvesting relay. The outage probability experienced by users in this network is characterized by taking the spatial randomness of user locations into consideration. In addition, the cooperation among users is modeled as a canonical coalitional game and the grand coalition is shown to be stable in the addressed scenario. Simulation results are provided to demonstrate the accuracy of the developed analytical results.
TL;DR: The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, stochastic nonlinearities, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant.
Abstract: This paper is concerned with the gain-constrained recursive filtering problem for a class of time-varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises. The stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case. The phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of Bernoulli distributed random variables taking values of 1 or 0, which means that the sensors may experience randomly occurring delays with individual delay characteristics. The process noise is finite-step autocorrelated. The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, stochastic nonlinearities, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant, where the filter gain satisfies a certain equality constraint. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre-specified filter gain constraint. A simulation example is provided to illustrate the effectiveness of the proposed filter design approach.
TL;DR: It is shown that the distribution of relative angles of motion between successive time intervals of random walks in two or more dimensions provides information about stochastic processes beyond the mean square displacement.
Abstract: Analyses of random walks traditionally use the mean square displacement (MSD) as an order parameter characterizing dynamics. We show that the distribution of relative angles of motion between successive time intervals of random walks in two or more dimensions provides information about stochastic processes beyond the MSD. We illustrate the behavior of this measure for common models and apply it to experimental particle tracking data. For a colloidal system, the distribution of relative angles reports sensitively on caging as the density varies. For transport mediated by molecular motors on filament networks in vitro and in vivo, we discover self-similar properties that cannot be described by existing models and discuss possible scenarios that can lead to the elucidated statistical features.
TL;DR: A stochastic process that may experience random reset events which suddenly bring the system to the starting value is considered and interesting properties emerge, like the existence of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior.
Abstract: In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.
TL;DR: A hybrid stochastic hierarchical equation of motion approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature.
Abstract: The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Forster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.
TL;DR: An input-output approach is employed to transform the time-delayed filtering error system into a feedback interconnection formulation and an improved version of bounded real lemma is obtained based on a Markovian Lyapunov-Krasovskii functional.
TL;DR: This work considers elliptic stochastic partial differential equations with random coefficients and employs reweighted l 1 minimization to recover the coefficients of the gPC expansion to find the approach suitable for problems for which the deterministic solver is very expensive.
TL;DR: In this paper, a transmission planning model for a system integrating a large amount of remote wind power is introduced, where uncertainties of wind availability and system load are represented by two dependent random variables in the optimization problem.
Abstract: This paper introduces a transmission planning model for a system integrating a large amount of remote wind power. We consider uncertainties of wind availability and system load, which are represented by two dependent random variables in the optimization problem. A two-stage stochastic model and sequential approximation approach are applied to solve our total cost minimization problem, which involves a sequence of stochastic optimization problems repeatedly solved with an updated approximation of random parameters until the rate of increment of optimal cost becomes smaller than a positive target value. A wind energy integration goal is achieved by penalizing wind curtailment. As a case study, the Electric Reliability Council of Texas (ERCOT) wind and load data, and a simplified model of its transmission system, is employed.
TL;DR: In this article, the authors proposed a sampling approach to estimate the distributions of the extreme value of the stochastic process, which is then used to replace the corresponding stochian process, and then the time-dependent reliability analysis is converted into its time-invariant counterpart.
Abstract: Maintaining high accuracy and efficiency is a challenging issue in time-dependent reliability analysis. In this work, an accurate and efficient method is proposed for limit-state functions with the following features: The limit-state function is implicit with respect to time. There is only one stochastic process in the input to the limit-sate function. The stochastic process could be either a general strength or a general stress variable so that the limit-state function is monotonic to the stochastic process. The new method employs a sampling approach to estimate the distributions of the extreme value of the stochastic process. The extreme value is then used to replace the corresponding stochastic process. Consequently the time-dependent reliability analysis is converted into its time-invariant counterpart. The commonly used time-invariant reliability method, the first order reliability method, is then applied to calculate the probability of failure over a given period of time. The results show that the proposed method significantly improves the accuracy and efficiency of time-dependent reliability analysis. [DOI: 10.1115/1.4023925]
TL;DR: A new method for clustering functional data is proposed under the name Funclust, which relies on the approximation of the notion of probability density for functional random variables, which generally does not exist and a parametric mixture model is proposed.
01 Jan 2013
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as discussed by the authors, and the first £ and £ price is net price subject to £ and US VAT.
Abstract: The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. C. Graham, D. Talay Stochastic Simulation and Monte Carlo Methods