On a Flow of Transformations of a Wiener Space

Abstract

In this chapter, we define, via Fourier transform, an ergodic flow of transformations of a Wiener space which preserves the law of the Ornstein–Uhlenbeck process and which interpolates the iterations of a transformation previously defined by Jeulin and Yor. Then, we give a more explicit expression for this flow, and we construct from it a continuous gaussian process indexed by ${\mathbb{R}}^{2}$, such that all its restriction obtained by fixing the first coordinate are Ornstein–Uhlenbeck processes.