Occupation times for countable Markov chains. I. Chains with discrete time
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One obtains the analogues of the “Ray's description” of the local time for one-dimensional Brownian motion, valid for arbitrary homogeneous Markov chains with discrete time and countable state space. Contrary to the case of the Brownian motion, one establishes the absence of the Markov property for the process of the occupation time in the case of the simplest one-dimensional symmetric random walk.
KeywordsMarkov Chain State Space Brownian Motion Random Walk Discrete Time
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- 1.K. Itô and H. P. McKean, Jr., Diffusion Processes and Their Sample Paths, Springer-Verlag, Berlin (1965).Google Scholar
- 2.I. J. Good, “The frequency count of a finite Markov chain and the transition to continuous time,” Ann. Math. Statist.,32, 41–48 (1961).Google Scholar
- 3.V. D. Barnett, “The joint distribution of occupation totals for a simple random walk,” J. Austral. Math. Soc.,4, 518–528 (1964).Google Scholar
- 4.W. S. Hsia, “The joint probability density function of the occupation time of a three-state problem,” J. Appl. Probab.,13, 57–64 (1976).Google Scholar
- 5.A. Plucińska, “On the joint limiting distribution of times spent in particular states by a Markov process,” Colloq. Math.,9, 347–360 (1962).Google Scholar
- 6.B. R. Bhat, “Some properties of regular Markov chains,” Ann. Math. Statist.,32, 59–71 (1961).Google Scholar