Abstract
The results of part I are carried over to Markov chains with continuous time. As opposed to the case of chains with discrete time, one establishes the Markov property of the occupation time process for the simplest one-dimensional symmetric random walk with continuous time.
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Literature cited
S. S. Vallander, “Occupation times for countable Markov chains. I. Chains with discrete time,” J. Sov. Math., No. 5,27 (1984).
K. L. Chung, Markov Chains with Stationary Transition Probabilities, Springer-Verlag, Berlin (1967).
K. Itô and H. P. McKean, Jr., Diffusion Processes and Their Sample Paths, Spinger-Verlag, Berlin (1965).
E. B. Dynkin, Markov Processes [in Russian], Fizmatgiz, Moscow (1963).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 56–64, 1983.
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Vallander, S.S. Occupation times for countable Markov chains. II. Chains with continuous time. J Math Sci 27, 3203–3208 (1984). https://doi.org/10.1007/BF01850666
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DOI: https://doi.org/10.1007/BF01850666