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.
作者
李治
徐丽平
何先平
LI Zhi;XU Liping;HE Xianping(School of Information and Mathematics,Yangtze University,Jingzhou,Hubei,434023,P.R.China)
出处
《数学进展》
CSCD
北大核心
2022年第3期538-550,共13页
Advances in Mathematics(China)
基金
Supported by NSFC(No.11901058).