This article is cited in 7 papers

On a probability of simultaneously extremes of two Gaussian nonstationary processes

A. Anshin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: This paper deals with the probability of simultaneous extremes of two Gaussian nonstationary processes $\mathbf{P}\bigl\{\max_{t\in[0,T]}X_1(t)>u,\ \max_{s\in[0,T]}X_2(s)>u\bigr\}$. The exact asymptotic representation for the probability is found as $u\to\infty$. The main tool for finding the asymptotics is a development of the double sum method.

Keywords: Gaussian nonstationary processes, extremum, double sum method.

Received: 30.12.2004

DOI: 10.4213/tvp86

 English version: Theory of Probability and its Applications, 2006, 50:3, 353–366

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