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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https://hal.archives-ouvertes.fr/hal-02433327
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Submitted on : Thursday, January 9, 2020 - 9:12:48 AM
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Loïc Chaumont, Jacek Małecki. Density behaviour related to Lévy processes. 2020. ⟨hal-02433327⟩

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