A connection between extreme value theory and long time approximation of SDEs

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Panloup, Fabien

关键词: Stochastic differential equation;    Jump process;    Invariant distribution;    Euler scheme;    Extreme value;   

DOI  :  10.1016/j.spa.2009.05.011

来源: Elsevier

【 摘 要 】

We consider a sequence (xi(n))(n >= 1) of i.i.d. random values residing in the domain of attraction of an extreme value distribution. For Such a sequence, there exist (a(n)) and (b(n)), with a(n) > 0 and b(n) is an element of R for every n >= 1, such that the sequence (X(n)) defined by X(n) = (max(xi(1),.... xi(n)) - b(n))/a(n) converges in distribution to a non-degenerated distribution. In this paper, we show that (X(n)) can be viewed as an Euler scheme with a decreasing step of an ergodic Markov process solution to a SDE with jumps and we derive a functional limit theorem for the sequence (X(n)) from some methods used in the long time numerical approximation of ergodic SDEs. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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