Extremes of q-Ornstein-Uhlenbeck processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Wang, Yizao¹ 

[1] Univ Cincinnati, Dept Math Sci, 2815 Commons Way, Cincinnati, OH 45221 USA

关键词: Markov process;    Self-similar process;    Tangent process;    Excursion probability;    Double-sum method;    Brown-Resnick process;    Semi-min-stable process;    q-Ornstein-Uhlenbeck process;   

DOI  :  10.1016/j.spa.2017.10.008

来源: Elsevier

【 摘 要 】

Two limit theorems are established on the extremes of a family of stationary Markov processes, known as q-Ornstein-Uhlenbeck processes with q is an element of (-1, 1). Both results are crucially based on the weak convergence of the tangent process at the lower boundary of the domain of the process, a positive self-similar Markov process little investigated so far in the literature. The first result is the asymptotic excursion probability established by the double-sum method, with an explicit formula for the Pickands constant in this context. The second result is a Brown-Resnick-type limit theorem on the minimum process of i.i.d. copies of the q-Ornstein-Uhlenbeck process: with appropriate scalings in both time and magnitude, a new semi-min-stable process arises in the limit. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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