TY - JOUR AU - Pei, Bin AU - Xu, Yong PY - 2016 DA - 2016/07/23 TI - On the non-Lipschitz stochastic differential equations driven by fractional Brownian motion JO - Advances in Difference Equations SP - 194 VL - 2016 IS - 1 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 $H\in(\frac{1}{2},1)$. 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. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-016-0916-1 DO - 10.1186/s13662-016-0916-1 ID - Pei2016 ER -