TY - JOUR
T1 - Mixed stochastic differential equations
T2 - Averaging principle result
AU - Han, Min
AU - Xu, Yong
AU - Pei, Bin
N1 - Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2021/2
Y1 - 2021/2
N2 - It is now known that, under a weaker condition than the Lipschitz one, the existence and uniqueness result for solutions of stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter H>1∕2 and a standard Brownian motion is obtained. Therefore, it is quite natural to ask whether or when the averaging principle result also holds. In this paper we study this problem using the tool of generalized Stieltjes integral and Bihari-type lemma.
AB - It is now known that, under a weaker condition than the Lipschitz one, the existence and uniqueness result for solutions of stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter H>1∕2 and a standard Brownian motion is obtained. Therefore, it is quite natural to ask whether or when the averaging principle result also holds. In this paper we study this problem using the tool of generalized Stieltjes integral and Bihari-type lemma.
KW - Averaging principles
KW - Fractional Brownian motion
KW - Generalized Stieltjes integral
KW - Non-Lipschitz condition
UR - https://www.scopus.com/pages/publications/85089999374
U2 - 10.1016/j.aml.2020.106705
DO - 10.1016/j.aml.2020.106705
M3 - 文章
AN - SCOPUS:85089999374
SN - 0893-9659
VL - 112
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 106705
ER -