Approximation properties for solutions to non-Lipschitz stochastic differential equations with Levy noise

作者：Xu, Yong^*; Pei, Bin; Li, Yongge

来源：Mathematical Methods in the Applied Sciences, 2015, 38(11): 2120-2131.

DOI：10.1002/mma.3208

• approximation theorems
• non-Lipschitz condition
• Levy noise
• stochastic differential equations
• stochastic functional differential equations

In this paper, we consider the non-Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Levy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non-Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems.

• 出版日期2015-7-30
• 单位西北工业大学