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Integral Equations in the Theory of Levy Processes

Lev Sakhnovich
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Abstract

In this article we consider the Levy processes and the corresponding semigroup. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the properties of a wide class of Levy processes (potential, quasi-potential, the probability of the Levy process remaining within the given domain, long time behavior, stable processes). We analyze in detail a number of concrete examples of the Levy processes (stable processes, the variance damped Levy processes, the variance gamma processes, the normal Gaussian process, the Meixner process, the compound Poisson process).

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Lev Sakhnovich. 2007-02-13. Integral Equations in the Theory of Levy Processes. https://arxiv.org/abs/math/0702378

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