Approximation of quantum Levy processes by quantum random walks

Lévy过程与随机游走的Wiener-Hopf分解的唯一性

The uniqueness of the Wiener-Hopf factorisation of Lévy processes and random walks

本文证明了无杀死的Lévy过程或随机游走的空间Wiener-Hopf分解的唯一性。

Integral Equations in the Theory of Levy Processes

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 Gaussia…