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Integro-Local Limit Theorems for Compound Renewal Processes Under Cramér’s Condition. II

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Abstract

We prove the statements that are formulated in the first part of this paper. As an auxiliary proposition, we establish an integro-local theorem for the renewal measure of a two-dimensional random walk.

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References

  1. Borovkov A. A. and Mogulskii A. A., “Integro-local limit theorems for compound renewal processes under Cramér’s condition. I,” Sib. Math. J., vol. 59, No. 3, 383–402 (2018).

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  2. Borovkov A. A. and Mogulskii A. A., “The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks,” Sib. Math. J., vol. 37, No. 4, 647–682 (1996).

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  3. Borovkov A. A., Asymptotic Analysis of Random Walks: Rapidly Decreasing Jumps [Russian], Fizmatlit, Moscow (2013).

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  4. Borovkov A. A., Probability, Gordon and Breach, Abingdon (1998).

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  5. Herve M., Several Complex Variables. Local Theory, Oxford Univ. Press, Bombay (1963).

    MATH  Google Scholar 

  6. Borovkov A. A. and Mogulskii A. A., “Large deviation principles for the finite-dimensional distributions of compound renewal processes,” Sib. Math. J., vol. 56, No. 1, 28–53 (2015).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. A. Borovkov & A. A. Mogulskii

Authors
  1. A. A. Borovkov
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  2. A. A. Mogulskii
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Correspondence to A. A. Borovkov.

Additional information

Original Russian Text © 2018 Borovkov A.A. and Mogulskii A.A.

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 4, pp. 736–758, July–August, 2018; DOI: 10.17377/smzh.2018.59.402.

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Borovkov, A.A., Mogulskii, A.A. Integro-Local Limit Theorems for Compound Renewal Processes Under Cramér’s Condition. II. Sib Math J 59, 578–597 (2018). https://doi.org/10.1134/S003744661804002X

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  • DOI: https://doi.org/10.1134/S003744661804002X

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