On Non-degenerate Chaos Processes

Abstract

We consider a process $\{X_t{\}}_{0\le t\le 1}$ in a fixed Wiener chaos ${\mathcal{H}}_n$. We establish some non-degenerate properties and related results for $\{X_t{\}}_{0\le t\le 1}$. As an application, we show that solution to SDE driven by $\{X_t{\}}_{0\le t\le 1}$ admits a density. Our approach relies on an interplay between Malliavin calculus and analysis on Wiener space.