分数布朗运动驱动的混合型随机微分方程的可行性  

Viability for Mixed Stochastic Differential Equations Driven by Fractional Brownian Motion

作　　者：李治[1] 徐丽平[1] 何先平[1] LI Zhi;XU Liping;HE Xianping(School of Information and Mathematics,Yangtze University,Jingzhou,Hubei,434023,P.R.China)

机构地区：[1]长江大学信息与数学学院,荆州湖北434023

出　　处：《数学进展》2022年第3期538-550,共13页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11901058).

摘　　要：本文着重研究了在一些弱条件下,由分数布朗运动驱动的混合型随机微分方程的闭凸集K的可行性.通过近似论证,我们证明了在线性增长条件下,由Hurst参数为1/2<H<1的分数布朗运动驱动的一类混合型随机微分方程解的存在性.因此,我们可以运用一些转换技术,在一些弱假设的情况下,获得所考虑的混合系统的可行性结果.最后给出一个例子来说明所获结果的有效性.In this paper,we focus on the viability of a close convex set K for mixed stochastic differential equations driven by fractional Brownian motion under some weak conditions.By approximation arguments,we prove the existence of solutions to a class of mixed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter 1/2<H<1 under the linear growth condition.As a result,we can obtain a viability result for the considered mixed systems with some weak hypotheses by making use of some transformation techniques.Lastly,an example is presented to illustrate the effectiveness of the obtained result.

关 键 词：可行性 线性增长 分数布朗运动 混合型随机微分方程 

分 类 号：O211.6[理学—概率论与数理统计]