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On the Exit of One Class of Random Walks from an Interval

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Abstract

We consider a random walk \(S_n = \sum {_{k \leqslant n} } \,\xi _k \;\left( {S_0 = 0} \right)\) for which the characteristic function of jumps ξ k satisfies the condition of almost semicontinuity. The problem of the exit of random walks S n of this type from a finite interval is studied.

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REFERENCES

  1. I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  2. A. V. Skorokhod, Random Processes with Independent Increments [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  3. V. S. Korolyuk, Boundary-Value Problems for Compound Poisson Processes [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  4. V. S. Korolyuk, N. S. Bratiichuk, and B. Pirdzhanov, Boundary-Value Problems for Random Walks [in Russian], Ylym, Ashkhabad (1987).

    Google Scholar 

  5. N. S. Bratiichuk and D. V. Gusak, Boundary-Value Problems for Processes with Independent Increments [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

  6. D. V. Husak, “Compound Poisson processes with two-sided reflection,” Ukr. Mat. Zh., 54, No.12, 1616–1625 (2002).

    Google Scholar 

  7. D. V. Husak, “Distribution of overjump functionals of a semicontinuous homogeneous process with independent increments,” Ukr. Mat. Zh., 54, No.3, 303–322 (2002).

    MATH  Google Scholar 

  8. D. V. Husak, “Boundary-value problems for processes with independent increments on finite Markov chains and for semi-Markov processes,” in: Works of the Institute of Mathematics of the Ukrainian Academy of Sciences [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (1998).

    Google Scholar 

  9. E. A. Pecherskii, “Some identities connected with the exit of a random walk from an interval and a semiinterval,” Teor. Ver. Primen., 19, No.1, 104–109 (1974).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv, Ukraine

    D. V. Husak

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  1. D. V. Husak
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1209–1217, September, 2005.

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Husak, D.V. On the Exit of One Class of Random Walks from an Interval. Ukr Math J 57, 1413–1423 (2005). https://doi.org/10.1007/s11253-006-0004-x

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  • DOI: https://doi.org/10.1007/s11253-006-0004-x

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