Pseudo-Poisson approximation for Markov chains

K. A. Borovkov and D. Pfeifer

Stochastic Processes and their Applications, 1996, vol. 61, issue 1, 163-180

Abstract: We consider the problem of approximating the distribution of a Markov chain with 'rare' transitions in an arbitrary state space by that of the corresponding pseudo-Poisson process. Sharp estimates for both first- and second-order approximations are obtained. The remarkable fact is that the convergence rate in this setup can be better than that in the ordinary Poisson theorem: the ergodicity of the embedded 'routing' Markov chain improves essentially the degree of approximation. This is of particular importance if the accumulated transition intensity of the chain is of a moderate size so that neither the usual estimates from the Poisson theorem nor the existence of a stationary distribution alone provide good approximation results. On the other hand, the estimates also improve the known results in the ordinary Poisson theorem.

Keywords: Poisson; approximation; Markov; chain; Pseudo-Poisson; process (search for similar items in EconPapers)
Date: 1996
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(95)00065-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:61:y:1996:i:1:p:163-180

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().