ON DISTRIBUTIONS OF EXPONENTIAL FUNCTIONALS OF THE PROCESSES WITH INDEPENDENT INCREMENTS

Lioudmila Vostrikova ()
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Lioudmila Vostrikova: LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique

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Abstract: The aim of this paper is to study the laws of the exponential functionals of the processes X with independent increments , namely I t = t 0 exp(−X s)ds, t ≥ 0, and also I ∞ = ∞ 0 exp(−X s)ds. Under suitable conditions we derive the integro-differential equations for the density of I t and I ∞. We give sufficient conditions for the existence of smooth density of the laws of these function-als. In the particular case of Levy processes these equations can be simplified and, in a number of cases, solved explicitly.

Keywords: process with independent increments; exponential functional; Kolmogorov-type equation; exponential func- tional; density; Kolmogorov-type equation MSC 2010 subject classifications: 60G51; 91G80 (search for similar items in EconPapers)
Date: 2020-02-03
Note: View the original document on HAL open archive server: https://hal.science/hal-01725776v2
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