Topic
Stochastic process
About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.
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TL;DR: In this article, it is pointed out that two contradictory definitions of fractional Brownian motion are well-established, one prevailing in the probabilistic literature, the other in the econometric literature, each associated with a different definition of nonstationary fractional time series, arising in functional limit theorems based on such series.
301 citations
TL;DR: A simple test, based on the analysis of the so-called p variations, which allows distinguishing between the two models on the basis of one realization of the unknown process, shows that it is likely that fractional Brownian motion is the underlying process.
Abstract: Fractional Brownian motion with Hurst index less then $1/2$ and continuous-time random walk with heavy tailed waiting times (and the corresponding fractional Fokker-Planck equation) are two different processes that lead to a subdiffusive behavior widespread in complex systems We propose a simple test, based on the analysis of the so-called $p$ variations, which allows distinguishing between the two models on the basis of one realization of the unknown process We apply the test to the data of Golding and Cox [Phys Rev Lett 96, 098102 (2006)], describing the motion of individual fluorescently labeled mRNA molecules inside live E coli cells It is found that the data does not follow heavy tailed continuous-time random walk The test shows that it is likely that fractional Brownian motion is the underlying process
300 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
01 Jan 1989
TL;DR: A precise mathematical framework is described to define a particular type of stochastic process, called a generalized semi-Markov process (GSMP), which captures the essential dynamical structure of a discrete event system.
Abstract: A precise mathematical framework for the study of discrete event systems is described. The idea is to define a particular type of stochastic process, called a generalized semi-Markov process (GSMP), which captures the essential dynamical structure of a discrete event system. An attempt is also made to give the flavor of the qualitative theory and numerical algorithms that can be obtained as a result of viewing discrete event systems as GSMPs. Likelihood ratio concepts for importance sampling are briefly described. >
299 citations
TL;DR: In this paper, a generalized polynomial chaos algorithm is proposed to model the input uncertainty and its propagation in flow-structure interactions, where the stochastic input is represented spectrally by employing orthogonal polynomials from the Askey scheme as the trial basis in the random space.
Abstract: We present a generalized polynomial chaos algorithm to model the input uncertainty and its propagation in flow-structure interactions. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as the trial basis in the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode. This approach is a generalization of the original polynomial chaos expansion, which was first introduced by N. Wiener and employs the Hermite polynomials (a subset of the Askey scheme) as the basis in random space. The algorithm is first applied to second-order oscillators to demonstrate convergence, and subsequently is coupled to incompressible Navier-Stokes equations. Error bars are obtained, similar to laboratory experiments, for the pressure distribution on the surface of a cylinder subject to vortex-induced vibrations
299 citations