Asymptotic results for exponential functionals of Lévy processes

Zenghu Li and Wei Xu

Stochastic Processes and their Applications, 2018, vol. 128, issue 1, 108-131

Abstract: The asymptotic behavior of expectations of some exponential functionals of a Lévy process is studied. The key point is the observation that the asymptotics only depend on the sample paths with slowly decreasing local infimum. We give not only the convergence rate but also the expression of the limiting coefficient. The latter is given in terms of some transformations of the Lévy process based on its renewal function. As an application, we give an exact evaluation of the decay rate of the survival probability of a continuous-state branching process in random environment with stable branching mechanism.

Keywords: Lévy process; Exponential functional; Laplace exponent; Branching process; Random environment; Survival probability (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:1:p:108-131

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DOI: 10.1016/j.spa.2017.04.005

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