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Preprints, Working Papers, ... Year : 2018

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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Dates and versions

hal-01730629 , version 1 (13-03-2018)
hal-01730629 , version 2 (29-03-2018)
hal-01730629 , version 3 (15-10-2018)

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