Levy's distributional property for symmetric Levy processes

摘要

We present the Levy's distributional property for symmetric Levy processeswith generating triplet $(0, 0,\nu)$ or $(\sigma>0, \gamma, \nu)$ where $\nu$is a symmetric measure on $R\backslash\{0\}$. This generalizes the classicalLevy's theorem about Brownian motions with drift.