IJPAM: Volume 69, No. 2 (2011)

LARGE DEVIATIONS APPLICATION TO EXIT
TIMES FOR SWITCHED MARKOV PROCESSES

Adina Oprisan$^1$, Andrzej Korzeniowski$^2$
$^1$Department of Mathematics and Computer Sciences
Barry University
Miami Shores, FL 33161, USA
e-mail: aoprisan@mail.barry.edu
$^2$Department of Mathematics
University of Texas at Arlington
P.O. Box 19408, Arlington, TX 76019, USA
e-mail: korzeniowski@uta.edu


Abstract. We study the effect of small perturbations on large time intervals for a family of stochastic additive functionals of Markov processes switched by jump Markov processes. The averaged limit process evolves deterministically on random time intervals according to the transition times of a stationary jump Markov process. Small perturbations essentially influence the behavior of the system and asymptotics of large deviations play an important role in analyzing it.

Received: March 10, 2011

AMS Subject Classification: 60F10, 60H10, 60B10

Key Words and Phrases: large deviations, additive functionals, jump Markov processes, average approximation, stability, exit times

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 2