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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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https://hal.archives-ouvertes.fr/hal-01725776
Contributor : Lioudmila Vostrikova Connect in order to contact the contributor
Submitted on : Monday, February 3, 2020 - 3:49:46 PM
Last modification on : Wednesday, November 3, 2021 - 9:15:29 AM
Long-term archiving on: : Monday, May 4, 2020 - 3:54:31 PM

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  • HAL Id : hal-01725776, version 2

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

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