TY - JOUR
T1 - Stochastic Averaging Principle for Mixed Stochastic Differential Equations
AU - Jing , Yuanyuan
AU - Peng , Yarong
AU - Li , Zhi
JO - Journal of Partial Differential Equations
VL - 3
SP - 223
EP - 239
PY - 2022
DA - 2022/06
SN - 35
DO - http://doi.org/10.4208/jpde.v35.n3.3
UR - https://global-sci.org/intro/article_detail/jpde/20773.html
KW - Averaging principle, mixed stochastic differential equation, discontinuous drift, fractional Brownian motion.
AB - <p style="text-align: justify;">In this paper, an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion, a fractional Brownian motion $B^{H}$ with the Hurst parameter $H&gt;\frac{1}{2}$ and a discontinuous drift was estimated. Under some proper assumptions, we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the Itô stochastic calculus.</p>