ASYMPTOTIC THEORY OF LARGE DEVIATIONS FOR MARKOV JUMP PROCESSES.

C. Knessl*, B. J. Matkowsky, Z. Schuss, C. Tier

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

We present a new asymptotic methods for the analysis of Markov jump processes. The methods, based on the WKB and other singular perturbation techniques, are applied directly to the Kolmogorov equations and not to approximate equations that come e. g. from diffusion approximations. For time homogeneous processes, we construct approximations to the stationary density function and the mean first passage time from a given domain. Examples involving a random walk and a problem in queueing theory are presented to illustrate our methods. For a class of time inhomogeneous processes, we construct long time approximations to the transition probability density function and the probability of large deviations from a stable state. The law of large numbers is obtained as a special case.

Original languageEnglish (US)
Pages (from-to)1006-1028
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume45
Issue number6
DOIs
StatePublished - Jan 1 1985

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint Dive into the research topics of 'ASYMPTOTIC THEORY OF LARGE DEVIATIONS FOR MARKOV JUMP PROCESSES.'. Together they form a unique fingerprint.

Cite this