非李普希兹条件下G-布朗运动驱动的随机微分方程的随机平均原理研究（英文）  

Stochastic Averaging for Non-Lipschitz Stochastic Differential Equations with G-Brownian Motion

作　　者：韩敏[1] 刘亚相[1] 

机构地区：[1]西北农林科技大学理学院,杨凌712100

出　　处：《应用概率统计》2017年第3期297-309,共13页Chinese Journal of Applied Probability and Statistics

摘　　要：在实际应用中,非李普希兹条件是比李普希兹条件更弱的一类条件.本文考虑非李普希兹条件下G-布朗运动驱动的随机微分方程,并建立了此类方程的随机平均原理,证明得出平均后方程的解在均方意义下收敛于原始方程的解.最后,给出一个具体实例来说明本文所建立的随机平均法的有效性.This paper concerns stochastic differential equations driven by G-Brownian motionunder non-Lipschitz condition which is a much weaker condition with a wider range of applica-tions. Stochastic averaging is established for such non-Lipschitz SDEs where an averaged system is presented to replace the original one in the sense of mean square. An example is presented to illustrate the averaging principle.

关 键 词：随机平均原理 G-布朗运动 非李普希兹条件 

分 类 号：O211.4[理学—概率论与数理统计]