Switching processes: Averaging principle, diffusion approximation and applications

DOI10.1007/BF00996931zbMath0827.60022OpenAlexW2062123308MaRDI QIDQ1897858

Vladimir V. Anisimov

Publication date: 4 December 1995

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00996931

zbMATH Keywords

functional limit theoremsdiffusion approximationstochastic differential equationssemi-Markov processesaveraging principledynamic systemsswitching processessemi-Markov switchingsqueueing systems and networks

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Diffusion processes (60J60) Markov renewal processes, semi-Markov processes (60K15) Functional limit theorems; invariance principles (60F17) Foundations of stochastic processes (60G05)

Related Items (21)

Averaging in Markov Models with Fast Semi-Markov Switches and Applications ⋮ Asymptotic Expansions for Solutions of Systems of Kolmogorov Backward Equations of Two-Time-Scale Switching Jump Diffusions ⋮ Asymptotic analysis of stochastic block replacement policies for multicomponent systems in a Markov environment ⋮ Increment processes and its stochastic exponential with Markov switching in Poisson approximation scheme ⋮ Stochastic approximation procedure in semi-Markov environment applied to alcohol consumption model ⋮ Asymptotic behavior of solutions of pulse systems with small parameter and Markov switchings. I: Uniform boundedness of solutions ⋮ Optimal state filtering of controllable systems with random structure ⋮ Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space ⋮ Special issue: 1st international workshop on retrial queues, WRQ '98. Complutense University of Madrid, Spain, September 22--24, 1998 ⋮ Switching stochastic models and applications in retrial queues ⋮ Asymptotical properties of Erlang queueing systems with a dependent Poisson input flow ⋮ Singularly perturbed Markov chains: Convergence and aggregation ⋮ Stochastic Liénard Equations with Random Switching and Two-time Scales ⋮ Continuous time Markov chains observed on an alternating renewal process with exponentially distributed durations ⋮ A Poisson Limit Theorem for Reliability Models Based on Markov Chains ⋮ Singularly perturbed diffusisons: Rapid switchings and fast diffusions. ⋮ Procedure of stochastic approximation for the diffusion process with semi-Markov switchings ⋮ Diffusion approximation of nonhomogeneous switching processes and its application to rate of convergence analysis of computational procedures ⋮ Reliability analysis of complex communication systems ⋮ The asymptotic properties of estimates of the parameters of nonlinear time series ⋮ Averaging methods for transient regimes in overloading retrial queueing systems.

Cites Work

• Random evolutions with underlying semi-Markov processes
• A central limit problem in random evolutions
• Random evolutions: A survey of results and problems
• Limit theorems for semigroups with perturbed generators, with applications to multiscaled random evolutions
• A limit theorem for perturbed operator semigroups with applications to random evolutions
• Applications of limit theorems for switching processes
• Averaging principle for the processes with fast switchings
• A Random Trotter Product Formula
• Multiplicative operator functionals of a Markov process
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