Showing papers on "Stochastic simulation published in 1995"

Random Vibrations: Theory and Practice

Abstract: Random Variables Random Processes in the Time Domain Fourier Transforms Random Processes in Frequency Domain Statistical Properties of Random Processes Vibration of Single-Degree-of-Freedom Systems Response of Single-Degree-of-Freedom Linear Systems to Random Environments Random Vibration of Multi-Degree-of-Freedom Systems Design to Avoid Structural Failures Due to Random Vibration Introduction to Parameter Estimation Time-Domain Estimation of Random Process Parameters Discrete Fourier Transform Frequency-Domain Estimation of Random Processes Appendices References Index

Stochastic simulation algorithms for dynamic probabilistic networks

Abstract: Stochastic simulation algorithms such as likelihood weighting often give fast, accurate approximations to posterior probabilities in probabilistic networks, and are the methods bf choice for very large networks. Unfortunately, the special characteristics of dynamic probabilistic networks (DPNs), which are used to represent stochastic temporal processes, mean that standard simulation algorithms perform very poorly. In essence, the simulation trials diverge further and further from reality as the process is observed over time. In this paper, we present simulation algorithms that use the evidence observed at each time step to push the set of trials back towards reality. The first algorithm, "evidence reversal" (ER) restructures each time slice of the DPN so that the evidence nodes for the slice become ancestors of the state variables. The second algorithm, called "survival of the fittest" sampling (SOF), "repopulates" the set of trials at each time step using a stochastic reproduction rate weighted by the likelihood of the evidence according to each trial. We compare the performance of each algorithm with likelihood weighting on the original network, and also investigate the benefits of combining the ER and SOF methods. The ER/SOF combination appears to maintain bounded error independent of the number of time steps in the simulation.

Using common random numbers for indifference-zone selection and multiple comparisons in simulation

Abstract: We present a general recipe for constructing experiment design and analysis procedures that simultaneously provide indifference-zone selection and multiple-comparison inference for choosing the best among k simulated systems. We then exhibit two such procedures that exploit the variance-reduction technique of common random numbers to reduce the sample size required to attain a fixed precision. One procedure is based on the Bonferroni inequality and is guaranteed to be statistically conservative. The other procedure is exact under a specific dependence structure, but may be slightly liberal otherwise. Both are easy to apply, requiring only simple calculations and tabled constants. We illustrate the procedures with a numerical example.

Stochastic simulation Bayesian approach to multitarget tracking

Abstract: A stochastic simulation Bayesian method for multitarget tracking is developed. This method uses a random sample in state space to represent the posterior state estimate distribution. The method is illustrated by simulations involving one target in dense clutter. Comparison with nearest-neighbours and probabilistic data association shows the superiority of the proposed method.

Bayesian sequential Gaussian simulation of lithology with non-linear data

Abstract: A multivariate stochastic simulation application that involves the mapping of a primary variable from a combination for sparse primary data and more densely sampled secondary data The method is applicable when the relationship between the simulated primary variable and one or more secondary variables is non-linear The method employs a Bayesian updating rule to build a local posterior distribution for the primary variable at each simulated location The posterior distribution is the product of a Gaussian kernel function obtained by simple kriging of the primary variable and a secondary probability function obtained directly from a scatter diagram between primary and secondary variables

Physical models as tests of randomness.

Abstract: We present and analyze in detail a test bench for random number sequences based on the use of physical models. The rst two tests, namely the cluster test and the autocorrelation test, are based on exactly known properties of the two{dimensional Ising model. The other two, the random walk test and the n{block test, are based on random walks on lattices. We have applied these tests to a number of commonly used pseudorandom number generators. The cluster test is shown to be particularly eecient in detecting periodic correlations on bit level, while the autocorrelation, the random walk, and the n{block tests are very well suited for studies of weak correlations in random number sequences. Based on the test results, we demonstrate the reasons behind errors in recent high precision Monte Carlo simulations, and discuss how these could be avoided.

Stochastic nagumo's viability theorem

Abstract: This paper is devoted to viability of random set-valued variables by stochastic differential equations, characterized in terms of stochastic tangent sets to random set-valued variables

Convergence of Random Sequences with Independent Random Indices II

Abstract: Necessary and sufficient conditions are obtained for the convergence of some statistics constructed from samples with random sizes.

Dynamic modelling of life table data.

Abstract: SUMMARY In this paper we formulate a dynamic model expressing the human life table data by using the firstpassage-time theory for a stochastic process. The model is derived analytically and then is applied to the mortality data in Belgium and France. A stochastic simulation is also performed for the 'health state function' proposed and the related stochastic paths. Furthermore the implications of the proposed model and the results derived for pension funds and option theory are discussed

Bayesian Inference in Cyclical Component Dynamic Linear Models

Abstract: Dynamic linear models (DLM's) with time-varying cyclical components are developed for the analysis of time series with persistent though time-varying cyclical behavior. The development covers inference on wavelengths of possibly several persistent cycles in nonstationary time series, permitting explicit time variation in amplitudes and phases of component waveforms, decomposition of stochastic inputs into purely observational noise and innovations that impact on the waveform characteristics, with extensions to incorporate ranges of (time-varying) time series and regression terms wihin the standard DLM context. Bayesian inference via iterative stochastic simulation methods is developed and illustrated. Some indications of model extensions and generalizations are given. In addition to the specific focus on cyclical component models, the development provides the basis for Bayesian inference, via stochastic simulation, for state evolution matrix parameters and variance components in DLM's, building o...

A Wold-Like Decomposition of Two-Dimensional Discrete Homogeneous Random Fields

Abstract: Imposing a total order on a regular two-dimensional discrete random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic field. The deterministic component is further orthogonally decomposed into a half-plane deterministic field and a countable number of mutually orthogonal evanescent fields. Each of the evanescent fields is generated by the column-to-column innovations of the deterministic field with respect to a different nonsymmetrical-half-plane total-ordering definition. The half-plane deterministic field has no innovations, nor column-to-column innovations, with respect to any nonsymmetrical-half-plane total-ordering definition. This decomposition results in a corresponding decomposition of the spectral measure of the regular random field into a countable sum of mutually singular spectral measures.

Evolution of systems in random media

Abstract: Introduction The Martingale Problem and Weak Convergence in Banach Space Random Processes and Martingales in Banach Space Operator Semi-Groups Markov Processes: Martingale Characterization Weak Convergence Martingale Problem in Banach Space Markov Renewal Processes Semi-Markov Processes Singular Perturbed Problems Perturbation of Reducible-Invertible Operators Phase Merging of Semi-Markov Processes Semi-Markov Random Evolutions Definition and Classification of Random Evolutions Stochastic Models of Systems Inhomogeneous Semi-Markov Random Evolutions Weak Convergence of Random Evolutions Relative Compactness of Random Evolutions Limiting Evolutions in Averaging and Diffusion Approximation Schemes Uniqueness of the Solution of the Martingale Problem Averaging and Diffusion Approximation of Random Evolution in Reducible Random Media Averaging of Stochastic Systems in Semi-Markov Random Media Compacts in Banach Spaces Traffic Processes Impulse Traffic Processes Additive Functionals Stochastic Differential Equations U-Statistical Processes Random Evolutions on Lie Groups Oscillations of a Harmonic Oscillator Waves in Conductors and Beams Diffusion Approximation of Stochastic Systems Traffic Processes Impulse Traffic Processes Additive Functionals U-Statistical Processes Random Motions on Lie Groups Normal Deviations of Semi-Markov Random Evolutions Random Evolution in Ergodic Media Stochastic Systems Random Evolution in Reducible Media Evolutionary Stochastic Systems in Reducible Media Rates of Convergence in the Limit Theorems for Random Evolutions Averaging Schemes for Random Evolutions Diffusion Approximation Scheme for Random Evolutions Averaging Scheme for Evolutionary Stochastic Systems in Random Media Diffusion Approximation Scheme for Evolutionary Stochastic Systems in Random Media Stability of Stochastic Systems Traffic Process in the Averaging Scheme Traffic Process in the Diffusion Approximation Scheme Impulse Traffic Process in the Averaging Scheme Impulse Traffic Process in the Diffusion Approximation Scheme Control of Evolutionary Stochastic Systems in Random Media Functionals of Uncontrolled Processes Cost Functionals Optimal Stochastic Control Bibliography Subject Index

Introduction to Random Processes in Engineering

Abstract: Review. Random Processes: Basic Concepts, Properties. Stationary Random Processes: Covariance and Spectrum. Response of Linear Systems to Random Inputs: Discrete--Time Models. Response of Linear Systems to Random Inputs: Continuous--Time Models. Time Averages and the Ergodic Principle. Sampling Principle and Interpolation. Simulation of Random Processes. Random Fields. Linear Filtering Theory. Problems. Notes and Comments. References. Index.

Fractals via Random Iterated Function Systems and Random Geometric Constructions

Abstract: I study random fractals which are obtained by means of random iterated function systems and more general random geometric constructions and estimate their Hausdorff dimensions. Random iterated function systems considered here generalize both random transformations and the well known deterministic iterated function systems. The paper is sequel to [Ki2] and it extends also some of the results from [PW] to the random situation employing the thermodynamic formalism for random subshifts of finite type.

Controlling correlations in parallel Monte Carlo

Abstract: Effects and detection of correlations in parallel Monte Carlo are discussed, on the assumption that each processor uses a sequence of truly random numbers, but the sequences are mutually correlated. Depending on the parallel implementation of the algorithm, effects may concern the mean value of the solution or only its variance. In the first case an alternative implementation of the algorithm is suggested. In the second — where it is possible to lose control of the result's accuracy — a control estimator is introduced which ensures correct computation of the variance. In this way one obtains reliability even when coprocessors are not independent. The same estimator, moreover, monitors the correlation transmitted from the source of random numbers to the results, i.e. the effect on computation velocity. Numerical examples show the sensitivity of the implemented control.

Random walks and stochastic differential equations

Abstract: The Wiener random walk is often studied in books on probability. It is a discrete process and classically, we cannot ask any question about the continuity or derivability of the trajectories or about the density of the process. The two results below are obtained by using discrete methods, but we are interested in the case of an infinitely large number of steps. With this hypothesis on the size of the variables, we prove some results which are similar to theorems on classical brownian motion. We want to take advantage of the simplicity of discrete concepts together with the simplicity of the analytical calculus. The link between the two classical methods is provided by nonstandard analysis.

Conditional simulation of non-Gaussian random fields for earthquake monitoring systems

Abstract: The problem of conditional simulation of random fields gained a significant interest recently due to its applications to urban earthquake monitoring. In this paper, for the first time in the literature, the method of conditional simulation of non-Gaussian random fields is developed. It combines previous techniques of iterative procedure of unconditional simulation of non-Gaussian fields, and the procedure of conditional simulation of Gaussian random fields. To contrast the agreement between the simulated correlation function and targeted correlation function, the numerical error is decomposed into two parts, namely, into simulation error and mapping error. Simulation error can be reduced by increasing number of samples while mapping error is eliminated by the suitable iteration procedure. In this paper univariate and time-independent random fields are considered. Numerical example shows that the correlation structure and probability distribution of the simulated random field have excellent agreements with given correlation structure and probability distribution, respectively.

Stochastic Simulation of Transport Phenomena

Abstract: In this paper, four examples are given to demonstrate how stochastic simulations can be used as a method to obtain numerical solutions to transport problems. The problems considered are two-dimensional heat conduction, mass diffusion with reaction, the start-up of Poiseuille flow, and Couette flow of a suspension of Hookean dumbbells. The first three examples are standard problems with well-known analytic solutions which can be used to verify the results of the stochastic simulation. The fourth example combines a Brownian dynamics simulation for Hookean dumbbells, a crude model of a dilute polymer suspension, and a stochastic simulation for the suspending, Newtonian fluid. These examples illustrate appropriate methods for handling source/sink terms and initial and boundary conditions. The stochastic simulation results compare well with the analytic solutions and other numerical solutions. The goal of this paper is to demonstrate the wide applicability of stochastic simulation as a numerical method for transport problems.