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Semimarkov walk on the composition of two renewal processes

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Ukrainian Mathematical Journal Aims and scope

Abstract

For a semi-Markov random walk on the composition of two renewal processes under the assumption that the positive jumps of the walk are distributed by an exponential law, an analytic expression is obtained for the generating function of the times of reaching level zero.

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Literature cited

  1. B. Pirdzhanov, “Random walk generated by two renewal processes,” Ukr. Mat. Zh.,30, No. 5, 680–685 (1978).

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  3. T. I. Nasirova, Semi-Markov Walk Processes [in Russian], Elm, Baku (1984).

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  4. Yu. S. Krutii, “Solution of two integral equations reduced to a matrix Riemann problem,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10, 18–21 (1989).

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

    B. Pirdzhanov

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  1. B. Pirdzhanov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1500–1508, November, 1990.

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Pirdzhanov, B. Semimarkov walk on the composition of two renewal processes. Ukr Math J 42, 1343–1350 (1990). https://doi.org/10.1007/BF01066190

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  • DOI: https://doi.org/10.1007/BF01066190

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