# On moments of integral exponential functionals of additive processes

Abstract : For real-valued additive process $(X_t)_{t\geq 0}$ a recursive equation is derived for the entire positive moments of functionals $I_{s,t}= \int _s^t\exp(-X_u)du,$ in case the Laplace exponent of $X_t$ exists for positive values of the parameter. From the equation emerges an easy-to-apply sufficient condition for the finiteness of the moments. As an application we study first hit processes of diffusions.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01730629
Contributor : Lioudmila Vostrikova <>
Submitted on : Monday, October 15, 2018 - 4:06:05 PM
Last modification on : Wednesday, December 19, 2018 - 2:08:04 PM
Document(s) archivé(s) le : Wednesday, January 16, 2019 - 12:46:40 PM

### Files

SPL_29_9.pdf
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### Identifiers

• HAL Id : hal-01730629, version 3
• ARXIV : 1803.04859

### Citation

Paavo Salminen, Lioudmila Vostrikova. On moments of integral exponential functionals of additive processes. 2018. ⟨hal-01730629v3⟩

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