Series representations and asymptotic expansions for the density of the supremum of a stable process

Details Series representations and asymptotic expansions for the density of the supremum of a stable process Series representations and asymptotic expansions for the density of the supremum of a stable process

2010-02-02

arxiv.org/abs/1002.0614v2

Mathematics

Probability

This paper has been withdrawn by the author. The results of this paper can now be found in Section 7 of the paper "On extrema

Scientific paper

We derive explicit asymptotic expansions of the density of the supremum of a
strictly stable process when the index $\alpha$ is not rational. In the case
when parameters $\alpha$ and $\rho=\p(X_1>0)$ satisfy $\rho+k=l/\alpha$ for
some integers $k,l \ge 1$ we prove that these asymptotic expansions are in fact
convergent series representations of the density of supremum.

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