A connection between extreme value theory and long time approximation of SDEs
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.
Year of publication: |
2009
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---|---|
Authors: | Panloup, Fabien |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 119.2009, 10, p. 3583-3607
|
Publisher: |
Elsevier |
Keywords: | Stochastic differential equation Jump process Invariant distribution Euler scheme Extreme value |
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