Poisson Approximation of Impulsive Recurrent Process with Semi-Markov Switching

In this article, the weak convergence of impulsive recurrent process with semi-Markov switching in the scheme of Poisson approximation is proved. Singular perturbation problem for the compensating operator of the extended Markov renewal process is used to prove the relative compactness.

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Bibliographic Details
Published in:Stochastic analysis and applications 2011-09, Vol.29 (5), p.769-778
Main Authors: Koroliuk, V. S., Limnios, N., Samoilenko, I. V.
Format: Article
Language:English
Subjects:
Approximation
Convergence
Exact sciences and technology
Impulsive recurrent process
Inference from stochastic processes
time series analysis
Insurance
Markov processes
Mathematical analysis
Mathematics
Operators
Poisson approximation
Primary 60K15, 60K37, 60B10
Probability and statistics
Probability theory and stochastic processes
Risk process
Sciences and techniques of general use
Secondary 60F17, 60H25
Semi-Markov process
Semimartingale
Singular perturbation
Statistics
Stochastic analysis
Stochastic processes
Stochasticity
Switching
Weak convergence
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Summary:In this article, the weak convergence of impulsive recurrent process with semi-Markov switching in the scheme of Poisson approximation is proved. Singular perturbation problem for the compensating operator of the extended Markov renewal process is used to prove the relative compactness.
ISSN:0736-2994
1532-9356
DOI:10.1080/07362994.2011.598780