Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space

DOI10.1214/aoap/1075828059zbMath1041.60061OpenAlexW2065983943MaRDI QIDQ1431563

Vladimir S. Korolyuk, Nikolaos Limnios

Publication date: 10 June 2004

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1075828059

zbMATH Keywords

diffusion approximationdynamic reliabilitystochastic evolutionary systemrewardMarkov process with locally independent incrementssplit state space

Mathematics Subject Classification ID

Random fields (60G60) Convergence of probability measures (60B10) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Functional limit theorems; invariance principles (60F17) Martingales and classical analysis (60G46) Local time and additive functionals (60J55)

Related Items (4)

Reliability of Semi-Markov Systems with Asymptotic Merging Phase Space ⋮ Reliability measures of semi-Markov systems with general state space ⋮ Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes ⋮ Queuing systems with semi-Markov flow in average and diffusion approximation schemes

Cites Work

• Increment processes and its stochastic exponential with Markov switching in Poisson approximation scheme
• Asymptotic behavior of Markov evolutions until absorption
• Martingale characterization of limit distributions in the space of functions without discontinuities of second kind
• Weak convergence methods and singularly perturbed stochastic control and filtering problems
• Monte-Carlo methods for the transport and diffusion equations
• Switching processes: Averaging principle, diffusion approximation and applications
• Applications of limit theorems for switching processes
• Stability of stochastic systems in the diffusion-approximation scheme
• Diffusion approximations in collective risk theory
• Semi-Markov processes and reliability
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