Extremes of Shepp statistics for the Wiener process
Journal article, 2008

Define Y(t)=max0≤s≤1W(t+s)−W(t)Y(t)=max0≤s≤1W(t+s)−W(t) , where W(·) is a standard Wiener process. We study the maximum of Y up to time T: MT=max0≤t≤TY(t)MT=max0≤t≤TY(t) and de termine an asymptotic expression for P(MT>u)P(MT>u) when u→ ∞. Further we establish the limiting Gumbel distribution of M T when T→ ∞ and present the corresponding normalization sequence.


Dmitrii Zholud

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg


1386-1999 (ISSN)

Vol. 11 4 339-351

Subject Categories

Probability Theory and Statistics



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2/6/2018 1