References
Takacs L., “On some recurrence equations in a Banach algebra,” Acta Sci. Math., 38, 399-416 (1976).
Lugavov V. S., “On the distribution of the sojourn time on a half-axis and the final position of a process with independent increments controlled by a Markov chain,” in: Trudy Inst. Mat. Sibirsk. Otdel. Akad. Nauk SSSR [in Russian], Nauka, Novosibirsk, 1984, 3, pp. 143-159.
Takacs L., “On fluctuations of sums of random variables,” Studies in Probability and Ergodic Theory. Advances in Mathematics Supplementary Studies, 2, 45-93 (1978).
Presman È. L., “The factorization methods and the boundary problem of sums of random variables on a Markov chain,” Izv. Akad. Nauk SSSR Ser. Mat., 33, No. 4, 861-900 (1969).
Borovkov A. A., Stochastic Processes in Queueing Theory [in Russian], Nauka, Moscow (1972).
Kemperman J. H. B., “A Wiener-Hopf type method for a general random walk with a two-sided boundary,” Ann. Math. Statist., 34, No. 4, 1168-1193 (1963).
Pecherskiľ E. A., “Some identities connected with the exit of a random walk from an interval and half-interval,” Teor. Veroyatnost. i Primenen., 19, No. 1, 104-119 (1974).
Lotov V. I., “On the asymptotics of distributions in two-sided boundary problems. I and II,” Teor. Veroyatnost. i Primenen., I: 24, No. 3, 475-485 (1979); II: 24, No. 4, 873-879 (1979).
Lotov V. I., “On the asymptotics of distributions connected with the exit of a nondiscrete random walk from an interval,” in: Trudy Inst. Mat. Sibirsk. Otdel. Akad. Nauk SSSR [in Russian], Nauka, Novosibirsk, 1982, 1, pp. 18-25.
Lugavov V. S., “On the sojourn time in a half-plane and a strip for processes controlled by a Markov chain,” in: Abstracts: Third School-Colloquium on Stochastic Methods, TVP, Moscow, 1996, pp. 108-109
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lugavov, V.S., Rogozin, B.A. Factorizations of the Sojourn Times of Semi-Markov Random Walks. Siberian Mathematical Journal 42, 332–347 (2001). https://doi.org/10.1023/A:1004845231582
Issue Date:
DOI: https://doi.org/10.1023/A:1004845231582