Extremes of Shepp statistics for the Wiener process

Abstract

We derive asymptotic behavior of the probability of high-level excursion for the maximal increment of the Wiener process. The result is essential for deriving the corresponding asymptotic formula for maximal increments of a Gaussian random walk, and also has potential applications in finance and insurance.

Supplementary materials

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Reference

Zholud, D. (2008). Extremes of Shepp statistics for the Wiener process, Extremes, Vol. 11, No. 4, pp. 339-351.

BiBTeX

@article{Zholud2008,
  Author = {Zholud, D.},
  Year = {2008},
  Title = {Extremes of Shepp statistics for the Wiener process},
  Journal = {Extremes},
  Volume = {11},
  Number = {4},
  Pages = {339--351}
}

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Update 2018