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
Stochastic Averaging for Non-Lipschitz SDEs with G-Brownian Motion
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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.Abstract: This paper concerns stochastic differential equations driven by G-Brownian motion under non-Lipschitz condition which is a much weaker condition with a wider range of applications. 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.