Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Das, Bikramjit¹  Engelke, Sebastian^2,3  Hashorva, En. Kelejd² 

[1] Singapore Univ Technol & Design, Singapore 138682, Singapore

[2] Univ Lausanne, Fac Business & Econ HEC Lausanne, CH-1015 Lausanne, Switzerland

[3] Ecole Polytech Fed Lausanne, FSB MATHAA STAT, CH-1015 Lausanne, Switzerland

关键词: Bessel process;    Brown-Resnick process;    Extreme value theory;    Functional convergence;   

DOI  :  10.1016/j.spa.2014.09.006

来源: Elsevier

【 摘 要 】

The convergence of properly time-scaled and normalized maxima of independent standard Brownian motions to the Brown-Resnick process is well-known in the literature. In this paper, we study the extremal functional behavior of non-Gaussian processes, namely squared Bessel processes and scalar products of Brownian motions. It is shown that maxima of independent samples of those processes converge weakly on the space of continuous functions to the Brown-Resnick process. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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