在非 Lipschitz係數條件及Levy noise 下隨機微分方程解存在性及唯一性

Abstract

我們在這篇論文主要探討的是Levy 擾動型隨機微分方程解的存在與唯一性的關係。我們更專注 在非Lipshcitz 條件下其解路徑唯一性的條件。其後介紹及比較近來有關路徑惟一在隨機微分方程相於對稱穩定過程的研究。

In this paper, we devote our attention to the relation of existence and uniqueness of stochastic differential equations with L'evy noise. Especially, we shall be concerned with the pathwise uniqueness of SDE with L'evy noises under non-Lipschitzian coefficients. We also describe, do and compare some of the resent work on pathwise uniqueness on stochastic differential equations with symmetric alpha-stable process, 1alpha<2.