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Time of the first departure from an interval for a continuous homogeneous random walk on a line

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Abstract

An investigation of a continuous homogeneous random walk possessing the Markov property with respect to times of passing any given level in a given direction. The existence and uniqueness of four functions characterizing the process is proved.

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Literature cited

  1. F. Spitzer, Principles of Random Walk, D. Van Nostrand, New York (1964).

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  2. B. V. Gnedenko, A Course in Probability Theory [in Russian], Moscow (1961).

  3. V. A. Ditkin and P. I. Kuznetsov, Manual of Operational Calculus [in Russian], Moscow-Leningrad (1951).

  4. B. P. Kharlamov, “Characterization of random functions by random images,” Zapiski Seminarov LOMI, No. 12, 165–196 (1969).

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Leningrad Branch, Academy of Sciences of the USSR, USSR

    B. P. Kharlamov

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  1. B. P. Kharlamov
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Translated from Matematicheskie Zametki, Vol. 9, No. 6, pp. 713–721, June, 1971.

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Kharlamov, B.P. Time of the first departure from an interval for a continuous homogeneous random walk on a line. Mathematical Notes of the Academy of Sciences of the USSR 9, 412–417 (1971). https://doi.org/10.1007/BF01094587

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  • DOI: https://doi.org/10.1007/BF01094587

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