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An asymptotic theory of large deviations for Markov jump processes. (English) Zbl 0582.60081
We present 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.

MSC:
60J75 Jump processes (MSC2010)
60F10 Large deviations
60K25 Queueing theory (aspects of probability theory)
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