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We derive asymptotic behavior of the probability of high-level excursion for the maximal increment of a Gaussian random walk.
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Extremes-of-Shepp-Statistics-for-Gaussian-Random-Walk.pdf
README.md

README.md

Extremes of Shepp statistics for Gaussian random walk

Abstract

We derive asymptotic behavior of the probability of high-level excursion for the maximal increment of a Gaussian random walk. The motivation for writing this paper comes from the problem of finding similarities between long biological sequences in Bioinformatics, however the result might also have suitable applications in other areas such as e.g. finance and insurance.

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Reference

Zholud, D. (2009). Extremes of Shepp statistics for Gaussian random walk, Extremes, Vol. 12, No. 1, pp. 1-17.

BiBTeX

@article{Zholud2009,
  Author = {Zholud, D.},
  Year = {2009},
  Title = {Extremes of Shepp statistics for Gaussian random walk},
  Journal = {Extremes},
  Volume = {12},
  Number = {1},
  Pages = {1--17}
}

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