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: A new model space MCMC method is developed based on extending the Bayesian variable selection approach which is usually applied to variable selection in regression models to state space models to focus on structural time series models including seasonal components, trend or intervention.
220 citations
Book•
01 Jan 1994
TL;DR: In this article, the authors focus on a class of processes with continuous sample paths that possess the Markov property and present an exposition based on the theory of stochastic analysis.
Abstract: Focusing on one of the major branches of probability theory, this book treats the large class of processes with continuous sample paths that possess the Markov property. The exposition is based on the theory of stochastic analysis, which uses such notions as stochastic differentials and stochastic integrals.
220 citations
Book•
01 Jan 1998
TL;DR: Systems, Models, and Simulation: Estimating Rare-Event Probabilities and Related Optimization Issues, and Sensitivity Analysis and Optimization of Discrete-Event Dynamic Systems: Distributed Parameters.
Abstract: CONVENTIONAL SIMULATION. Systems, Models, and Simulation. Random Numbers, Variates, and Stochastic Process Generation. Output Analysis of Discrete-Event Systems via Simulation. Variance Reduction Techniques. MODERN SIMULATION. Sensitivity Analysis and Optimization of Discrete-Event Static Systems (DESS). Sensitivity Analysis and Optimization of Discrete-Event Dynamic Systems: Distributed Parameters. Sensitivity of Analysis of Discrete-Event Dynamic Systems: Structural Parameters. Response Surface Methodology via the Score Function Method. Estimating Rare-Event Probabilities and Related Optimization Issues. Index.
220 citations
TL;DR: The displacement correlation function is defined and it is found that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.
Abstract: Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.
220 citations