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Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case

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Abstract

Under the inhomogeneous case wemean the case when one or several (arbitrarily many) inhomogeneous summands are added to the sum of independent identically distributed vectors. We find necessary and sufficient conditions under which the large deviation principles for such sums and the corresponding renewal functions have the same form that in the homogeneous case.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    A. A. Borovkov & A. A. Mogul’skiĭ

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    A. A. Borovkov & A. A. Mogul’skiĭ

Authors
  1. A. A. Borovkov
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  2. A. A. Mogul’skiĭ
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Correspondence to A. A. Borovkov.

Additional information

Original Russian Text © A.A. Borovkov, A.A. Mogul’skiĭ, 2014, published in Matematicheskie Trudy, 2014, Vol. 17, No. 2, pp. 84–101.

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Borovkov, A.A., Mogul’skiĭ, A.A. Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case. Sib. Adv. Math. 25, 255–267 (2015). https://doi.org/10.3103/S1055134415040033

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  • DOI: https://doi.org/10.3103/S1055134415040033

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