Limiting distributions of functionals of Markov chains

Karandikar, Rajeeva L. ; Kulkarni, Vidyadhar G. (1985) Limiting distributions of functionals of Markov chains Stochastic Processes and their Applications, 19 (2). pp. 225-235. ISSN 0304-4149

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Let \s{Xn, n □ 0\s} and \s{Yn, n □ 0\s} be two stochastic processes such that Yn depends on Xn in a stationary manner, i.e. P(Yn □ A\vbXn) does not depend on n. Sufficient conditions are derived for Yn to have a limiting distribution. If Xn is a Markov chain with stationary transition probabilities and Yn = f(Xn,..., Xn+k) then Yn depends on Xn is a stationary way. Two situations are considered: (i) \s{Xn, n □ 0\s} has a limiting distribution (ii) \s{Xn, n □ 0\s} does not have a limiting distribution and exits every finite set with probability 1. Several examples are considered including that of a non-homogeneous Poisson process with periodic rate function where we obtain the limiting distribution of the interevent times.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Markov Chains; Limiting Distributions; Periodic Nonhomogeneous Poisson Processes
ID Code:73315
Deposited On:02 Dec 2011 08:20
Last Modified:02 Dec 2011 08:20

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