论文标题
黄色Zakai类型的粗糙随机动力学系统的近似值通过光滑的噪声
Wong-Zakai type approximations of rough random dynamical systems by smooth noise
论文作者
论文摘要
本文致力于由一类粗糙的微分方程的平稳和固定的Wong-Zakai近似值，该等级由几何分数Brownian Rough Path $ \BoldsymbolΩ$带有Hurst Index $ H \ in（\ frac {1} {1} {1} {3} {3} {3} {3} {3} {3}，\ frac {1} {1} {1} {2} $ bold $ bold $。 $ \boldsymbolΩ$通过概率参数，然后使用粗糙路径理论在任何有限的间隔上获得解决方案的Wong-Zakai近似值。 $δ\ rightarrow 0 $。
This paper is devoted to the smooth and stationary Wong-Zakai approximations for a class of rough differential equations driven by a geometric fractional Brownian rough path $\boldsymbolω$ with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$. We first construct the approximation $\boldsymbolω_δ$ of $\boldsymbolω$ by probabilistic arguments, and then using the rough path theory to obtain the Wong-Zakai approximation for the solution on any finite interval. Finally, both the original system and approximative system generate a continuous random dynamical systems $φ$ and $φ^δ$. As a consequence of the Wong-Zakai approximation of the solution, $φ^δ$ converges to $φ$ as $δ\rightarrow 0$.
