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

Fabien Panloup

Stochastic Processes and their Applications, 2009, vol. 119, issue 10, 3583-3607

Abstract: 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 (an) and (bn), with an>0 and for every n>=1, such that the sequence (Xn) defined by Xn=(max([xi]1,...,[xi]n)-bn)/an converges in distribution to a non-degenerated distribution. In this paper, we show that (Xn) 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 (Xn) from some methods used in the long time numerical approximation of ergodic SDEs.

Keywords: Stochastic; differential; equation; Jump; process; Invariant; distribution; Euler; scheme; Extreme; value (search for similar items in EconPapers)
Date: 2009
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