论文标题
在非脱位混乱过程中
On Non-degenerate Chaos Processes
论文作者
论文摘要
我们考虑一个固定的Wiener Chaos $ \ Mathcal {H} _n $中的过程$ \ {x_t \} _ {0 \ leq t \ leq 1} $。我们为$ \ {x_t \} _ {0 \ leq t \ leq 1} $建立了一些非脱位属性和相关结果。作为一个应用程序，我们显示了由$ \ {x_t \} _ {0 \ leq t \ leq 1} $驱动的SDE解决方案。我们的方法取决于Malliavin演算与Wiener空间分析之间的相互作用。
We consider a process $\{X_t\}_{0\leq t\leq 1}$ in a fixed Wiener chaos $\mathcal{H}_n$. We establish some non-degenerate properties and related results for $\{X_t\}_{0\leq t\leq 1}$. As an application, we show that solution to SDE driven by $\{X_t\}_{0\leq t\leq 1}$ admits a density. Our approach relies on an interplay between Malliavin calculus and analysis on Wiener space.
