分数Brown 运动驱动的非 Lipschitz随机微分方程

讨论了一类带分数Brown 运动的非Lipschitz 增长的随机微分方程适应解的存在唯一性。关于分数 Brown 运动的随机积分有多种定义,本文使用一种广义 Stieltjes积分定义方法,利用这种积分的性质,建立了一类由标准 Brown 运动和一个 Hurst 指数H ∈(1/2,1)的分数Brown 运动共同驱动的、系数为非Lipschitz 增长的随机微分方程适应解的存在唯一性定理。

Non-Lipschitz stochastic differential equations driven by fractional Brownian

In this paper, we discuss the existence and uniqueness of a class of non-Lipschitzd stochastic differential equations driven by fractional Brownian motion with Hurst parameter H ∈( 12 , 1). So far, there are several ways to define stochastic integrals with respect to FBM. In this paper, we define stochastic integrals with respect to FBM as a generalized Stieltjes integral. We give a theorem of existence and uniqueness for SDE with coe?cients allowed to have a non-Lipschitzd growth.