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Preprints, Working Papers, ... Year : 2020

Density behaviour related to Lévy processes

Abstract

Let p t (x), f t (x) and q * t (x) be the densities at time t of a real Lévy process, its running supremum and the entrance law of the reflected excursions at the infimum. We provide relationships between the asymptotic behaviour of p t (x), f t (x) and q * t (x), when t is small and x is large. Then for large x, these asymptotic behaviours are compared to this of the density of the Lévy measure. We show in particular that, under mild conditions, if p t (x) is comparable to tν(x), as t → 0 and x → ∞, then so is f t (x).
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Dates and versions

hal-02433327 , version 1 (09-01-2020)

Identifiers

  • HAL Id : hal-02433327 , version 1

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Loïc Chaumont, Jacek Małecki. Density behaviour related to Lévy processes. 2020. ⟨hal-02433327⟩
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