Abstract
One considers continuous semi-Markov processes on the line. One investigates necessary conditions for the representation of the semi-Markov transition functions in the form of the solutions of second-order differential equations.
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Literature cited
E. Kamke, Handbook of Ordinary Differential Equations, Chelsea Publ.
I. P. Natanson, Theory of Functions of a Real Variable [in Russian], Nauka, Moscow (1974).
G. Sansone, Equazioni Differenzialinel Campo Reale, I, Zanichelli, Bologna (1948).
B. P. Kharlamov, “Random processes with semi-Markov chains of hitting times,” J. Sov. Math.,9, No. 1 (1978).
B. P. Kharlamov, “Exit sequences and continuous semi-Markov processes on the line,” J. Sov. Math.,27, No. 5 (1984).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 190–205, 1983.
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Kharlamov, B.P. Transition functions of a continuous semi-Markov process on the line. J Math Sci 27, 3304–3315 (1984). https://doi.org/10.1007/BF01850682
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DOI: https://doi.org/10.1007/BF01850682