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Extremes of Shepp statistics for the Wiener process |
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| Authors: | Dmitrii Zholud |
| Affiliation: | 1. Department of Mathematical Statistics, Chalmers University of Technology and G?teborg University, G?teborg, Sweden |
| Abstract: | Define  , where W(·) is a standard Wiener process. We study the maximum of Y up to time T:  and de termine an asymptotic expression for  when u→ ∞. Further we establish the limiting Gumbel distribution of M T when T→ ∞ and present the corresponding normalization sequence. |
| Keywords: | Wiener process increments Shepp statistics High level excursions Analysis of extreme values Large deviations Asymptotic behavior Distribution tail Gumbel law Limit theorems Weak theorems |
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