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

الأصل · EN

We derive explicit asymptotic expansions of the density of the supremum of a strictly stable process when the index α is not rational. In the case when parameters α and ρ=(X₁>0) satisfy ρ+k=l/α for some integers k,l ≥ 1 we prove that these asymptotic expansions are in fact convergent series representations of the density of supremum.