论文标题
与本地Lipschitz系数的非自治混合随机微分方程的随机平均
Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients
论文作者
论文摘要
本文研究了一个非自主慢速系统，该系统由具有局部Lipschitz系数的随机微分方程（SDE）概括，并受到标准的Brownian运动（BM）和分数Brownian Motion（FBM），并带有Hurst参数1/2 <H <1。我们专注于如何相对于BM和FBM以及本地Lispchitz的连续性处理两种类型的积分。路径方法和ITO随机演算与停止时间的技术结合，以确定定义平均方程的平均原理。然后，验证了原始慢速系统的慢组分将在均等意义上收敛到所提出的平均方程的解决方案。
This paper investigates a non-autonomous slow-fast system, which is generalized by stochastic differential equations (SDEs) with locally Lipschitz coefficients, subjected to standard Brownian motion (Bm) and fractional Brownian motion (fBm) with Hurst parameter 1/2<H<1. We concentrate on how to handle both types of integrals with respect to Bm and fBm and the locally Lispchitz continuity. The pathwise approach and the Ito stochastic calculus are combined with the technique of stopping time to establish the averaging principle where the averaged equation is defined. Then, the slow component of the original slow-fast system converges to the solution of the proposed averaged equation in the mean square sense is verified.
