Skip to main content
Log in

Limit theorems in a boundary crossing problems for random walks

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. V. S. Korolyuk and Yu. V. Borovskikh, Analytic Problems of the Asymptotics of Probability Distributions [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  2. V. I. Lotov, “On the asymptotics of distributions in two-sided boundary problems for random walks defined on a Markov chain,” Siberian Adv. Math.,1, No. 3, 26–51 (1991).

    MATH  Google Scholar 

  3. V. I. Lotov, “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).

    MATH  Google Scholar 

  4. V. I. Lotov, “On the asymptotics of distributions connected with the exit of a nondiscrete random walk from an interval,” in: Probability Limit Theorems and Related Problems. Vol. 1 (Trudy Inst. Mat.) [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk, 1982, pp. 18–25.

    Google Scholar 

  5. S. V. Nagaev, “An estimate for the convergence rate of the absorption probability,” Teor. Veroyatnost. i Primenen.,16, No. 1, 140–148 (1971).

    Google Scholar 

  6. A. A. Borovkov, “New limit theorems for boundary problems for sums of independent summands,” Sibirsk. Mat. Zh.,3, No. 5, 645–694 (1962).

    MATH  Google Scholar 

  7. J. H. B. Kemperman, “A Wiener-Hopf type method for a general random walk with a two-sided boundary,” Ann. Math. Statist.,34, No. 4, 1168–1193 (1963).

    Google Scholar 

  8. E. A. Pecherskiî, “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).

    Google Scholar 

  9. H. Bateman and A. Erdélyi, Tables of Integral Transformations. Vol. 1 [Russian translation], Nauka, Moscow (1968).

    Google Scholar 

  10. A. A. Borovkov and B. A. Rogozin, “Boundary problems for some two-dimensional random walks,” Teor. Veroyatnost. i Primenen.,9, No. 3, 401–430 (1964).

    MATH  Google Scholar 

Download references

Authors

Additional information

This research was supported by the Russian Foundation for Basic Research (Grants 96-01-01533 and 96-15-96295).

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 5, pp. 1095–1108, September–October, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lotov, V.I. Limit theorems in a boundary crossing problems for random walks. Sib Math J 40, 925–937 (1999). https://doi.org/10.1007/BF02674722

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02674722

Keywords

Navigation