论文标题
具有加性分数噪声的随机微分方程的弱解
Weak solutions for stochastic differential equations with additive fractional noise
论文作者
论文摘要
我们提供了一种新的方法来证明存在\ [dx_t = f（t，x_t）dt + g（t）db^h_t \]的弱解决方案，其中$ b^h_t $是分数的布朗尼运动，具有可分离的希尔伯特空间中可分开的Hilbert Space的值，用于合适的功能$ f $ f $和$ g $。我们的想法是使用隐式函数定理和分数布朗运动的缩放特性，以便为该方程获得弱解。
We give a new approach to prove the existence of a weak solution of \[dx_t = f(t,x_t)dt + g(t)dB^H_t\] where $B^H_t$ is a fractional Brownian motion with values in a separable Hilbert space for suitable functions $f$ and $g$. Our idea is to use the implicit function theorem and the scaling property of the fractional Brownian motion in order to obtain a weak solution for this equation.
