Occupation times for countable Markov chains. I. Chains with discrete time
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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