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ON DISTRIBUTIONS OF EXPONENTIAL FUNCTIONALS OF THE PROCESSES WITH INDEPENDENT INCREMENTS

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.
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Dates and versions

hal-01725776 , version 1 (07-03-2018)
hal-01725776 , version 2 (03-02-2020)

Identifiers

  • HAL Id : hal-01725776 , version 2

Cite

Lioudmila Vostrikova. ON DISTRIBUTIONS OF EXPONENTIAL FUNCTIONALS OF THE PROCESSES WITH INDEPENDENT INCREMENTS. 2020. ⟨hal-01725776v2⟩
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