TY - JOUR
T1 - On the non-Lipschitz stochastic differential equations driven by fractional Brownian motion
AU - Pei, Bin
AU - Xu, Yong
N1 - Publisher Copyright:
© 2016, Pei and Xu.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - In this paper, we use a successive approximation method to prove the existence and uniqueness theorems of solutions to non-Lipschitz stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) with the Hurst parameter H∈(12,1). The non-Lipschitz condition which is motivated by a wider range of applications is much weaker than the Lipschitz one. Due to the fact that the stochastic integral with respect to fBm is no longer a martingale, we definitely lost good inequalities such as the Burkholder-Davis-Gundy inequality which is crucial for SDEs driven by Brownian motion. This point motivates us to carry out the present study.
AB - In this paper, we use a successive approximation method to prove the existence and uniqueness theorems of solutions to non-Lipschitz stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) with the Hurst parameter H∈(12,1). The non-Lipschitz condition which is motivated by a wider range of applications is much weaker than the Lipschitz one. Due to the fact that the stochastic integral with respect to fBm is no longer a martingale, we definitely lost good inequalities such as the Burkholder-Davis-Gundy inequality which is crucial for SDEs driven by Brownian motion. This point motivates us to carry out the present study.
KW - existence and uniqueness
KW - fractional Brownian motion
KW - non-Lipschitz condition
KW - stochastic differential equations
UR - http://www.scopus.com/inward/record.url?scp=84979231299&partnerID=8YFLogxK
U2 - 10.1186/s13662-016-0916-1
DO - 10.1186/s13662-016-0916-1
M3 - 文章
AN - SCOPUS:84979231299
SN - 1687-1839
VL - 2016
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 194
ER -