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Stability theorems and the second-order asymptotics in threshold phenomena for boundary functionals of random walks

Abstract

In Section 1, we prove stability theorems for a series of boundary functionals of random walks. In Section 2, we suggest a new simpler proof of the theorem on threshold phenomena for the distribution of the maximum of the consecutive sums of random variables. In Section 3, we find the second-order asymptotics for this distribution under the assumption that the third moments of the random variables exist.

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Correspondence to A. A. Borovkov.

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Original Russian Text ©A. A. Borovkov, 2016, published in Matematicheskie Trudy, 2016, Vol. 19, No. 1, pp. 46–69.

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Borovkov, A.A. Stability theorems and the second-order asymptotics in threshold phenomena for boundary functionals of random walks. Sib. Adv. Math. 26, 231–246 (2016). https://doi.org/10.3103/S1055134416040015

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Keywords

  • random walks
  • boundary functionals
  • stability theorems
  • threshold phenomena
  • second-order asymptotics
  • asymptotic expansions