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Limiting distributions of functionals of Markov chains

Author

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  • Karandikar, Rajeeva L.
  • Kulkarni, Vidyadhar G.

Abstract

Let \s{Xn, n [greater-or-equal, slanted] 0\s} and \s{Yn, n [greater-or-equal, slanted] 0\s} be two stochastic processes such that Yn depends on Xn in a stationary manner, i.e. P(Yn [epsilon] 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 [greater-or-equal, slanted] 0\s} has a limiting distribution (ii) \s{Xn, n [greater-or-equal, slanted] 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.

Suggested Citation

  • Karandikar, Rajeeva L. & Kulkarni, Vidyadhar G., 1985. "Limiting distributions of functionals of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 225-235, April.
    • Handle: RePEc:eee:spapps:v:19:y:1985:i:2:p:225-235
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