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February 2004 Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space
Vladimir S. Korolyuk, Nikolaos Limnios
Ann. Appl. Probab. 14(1): 489-516 (February 2004). DOI: 10.1214/aoap/1075828059

Abstract

Stochastic evolutionary systems of additive functional type, described by processes with locally independent increments, are considered with Markov switching in an asymptotic split state space having a stoppage state. The average and diffusion approximation limit theorems are established in both single and double merging. The proofs of these results are obtained using a singular perturbation approach of linear reducible--invertible operators and the tightness of processes. Particular cases of these systems including integral functionals, dynamic systems, storage processes and compound Poisson processes are also considered. The application of limit theorems in reliability and reward problems is discussed.

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Vladimir S. Korolyuk. Nikolaos Limnios. "Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space." Ann. Appl. Probab. 14 (1) 489 - 516, February 2004. https://doi.org/10.1214/aoap/1075828059

Information

Published: February 2004
First available in Project Euclid: 3 February 2004

zbMATH: 1041.60061
MathSciNet: MR2023028
Digital Object Identifier: 10.1214/aoap/1075828059

Subjects:
Primary: 60B10 , 60F17 , 60J55 , 60K10
Secondary: 60G46 , 60G60

Keywords: diffusion approximation , dynamic reliability , Markov process with locally independent increments , reward , split state space , Stochastic evolutionary system

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 1 • February 2004
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