Exponential functionals of spectrally one-sided l{\'e}vy processes conditioned to stay positive

Grégoire Véchambre; Grégoire Vechambre

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arXiv · 1507.02949

Exponential functionals of spectrally one-sided l{\'e}vy processes conditioned to stay positive

Grégoire Véchambre·Grégoire Vechambre

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Abstract

We study the properties of the exponential functional $\int\_0^{+ \infty} e^{- X^{\uparrow} (t)}dt$ where $X^{\uparrow}$ is a spectrally one-sided L{\'e}vy process conditioned to stay positive. In particular, we study finiteness, self-decomposability, existence of finite exponential moments, asymptotic tail at $0$ and smoothness of the density.

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Grégoire Véchambre, Grégoire Vechambre. 2015-07-10. Exponential functionals of spectrally one-sided l{\'e}vy processes conditioned to stay positive. https://arxiv.org/abs/1507.02949

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