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On the Asymptotics of the Sojourn Probability of a Poisson Process between Two Nonlinear Boundaries That Move Away from One Another

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Abstract

We obtain the complete asymptotic decomposition of the sojourn probability of a homogeneous Poisson process inside a domain with curvilinear boundaries. The coefficients of this decomposition are determined by the solutions of parabolic problems with one and two boundaries.

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REFERENCES

  1. A. V. Skorokhod, Random Processes with Independent Increments [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  2. A. Dvoretsky, J. Kiefer, and J. Wolfowitz, “Sequential decision problem for processes with continuous time-parameter. Testing hypotheses,” Ann. Math. Stat. 24, 254–264 (1953).

    Google Scholar 

  3. J. de Lucia and H. V. Poor, “The moment generating function of the stopping time for a linearly stopped Poisson process,” Commun. Statist.-Stochast. Models 13, No. 2, 275–292 (1997).

    Google Scholar 

  4. C. R. Loader, “Boundary crossing probabilities for locally Poisson processes,” Ann. Appl. Probab. 2, No. 1, 199–228 (1992).

    Google Scholar 

  5. V. S. Korolyuk, “On the asymptotic behavior of certain functionals in the lattice scheme of walks,” Teor. Ver. Primen. 6, No. 3, 334–341 (1961).

    Google Scholar 

  6. V. S. Korolyuk and D. V. Gusak, “On the asymptotic behavior of distributions of maximum deviations in Poisson processes,” Ukr. Mat. Zh. 14, No. 2, 138–144 (1962).

    Google Scholar 

  7. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  8. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977).

    Google Scholar 

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Authors and Affiliations

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

    V. A. Gasanenko

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  1. V. A. Gasanenko
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Gasanenko, V.A. On the Asymptotics of the Sojourn Probability of a Poisson Process between Two Nonlinear Boundaries That Move Away from One Another. Ukrainian Mathematical Journal 53, 15–25 (2001). https://doi.org/10.1023/A:1010428515104

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  • DOI: https://doi.org/10.1023/A:1010428515104

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