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Stochastic systems

Stochastic differential equati. --- Stochastic differential equations. --- Stochastic systems. --- Systems, Stochastic --- Stochastic processes --- System analysis --- Differential equations --- Fokker-Planck equation --- Stochastic differential equations

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Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of the system (its state and evolution), and relate those to the input parameters of the system and initial data. This book i

Stochastic systems. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Systems, Stochastic --- Stochastic processes --- System analysis

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Numerical approximation theory --- 519.25 --- 519.7 --- Numerical analysis --- -Stochastic systems --- -Systems, Stochastic --- Stochastic processes --- System analysis --- Mathematical analysis --- Statistical data handling --- Mathematical cybernetics --- Addresses, essays, lectures --- Numerical analysis. --- Stochastic systems. --- -Statistical data handling --- 519.7 Mathematical cybernetics --- 519.25 Statistical data handling --- -519.7 Mathematical cybernetics --- Systems, Stochastic --- Stochastic systems

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The book is devoted to studies of quasi-stationary phenomena in nonlinearly perturbed stochastic systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on new types of asymptotic expansions for perturbed renewal equation and recurrence algorithms for construction of asymptotic expansions for Markov type processes with absorption are presented. Asymptotic expansions are given in mixed ergodic (for processes) and large deviation theorems (for absorption times) for nonlinearly perturbed regenerative processes, semi-Markov processes, and Markov chains. Applications to analysis of quasi-stationary phenomena in nonlinearly perturbed queueing systems, population dynamics and epidemic models, and for risk processes are presented. The book also contains an extended bibliography of works in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications and may be also useful for doctoral and advanced undergraduate students.

Quasistationarer Zustand --- Stochastisches System --- Storungstheorie --- Stochastic systems. --- Stochastic processes. --- Random processes --- Systems, Stochastic --- Probabilities --- Stochastic processes --- System analysis --- Markov Chains. --- Nonlinearly Perturbed Regenerative Processes. --- Renewal Equation. --- Semi-Markov Processes.

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Stochastic control theory. --- Stochastic systems. --- Discrete-time systems. --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Systems, Stochastic --- Stochastic processes --- Control theory