Some Ergodic Theorems for Random Rotations on Wiener Space

TL;DR

This paper investigates the ergodic and mixing properties of measure-preserving transformations on Wiener space generated by random unitary operators on the Cameron-Martin space.

Contribution

It introduces new ergodic theorems for transformations induced by random rotations on Wiener space, expanding understanding of their long-term behavior.

Findings

Established conditions for ergodicity of random rotations on Wiener space.

Proved mixing properties for certain classes of measure-preserving transformations.

Provided insights into the structure of transformations generated by random unitary operators.

Abstract

In this paper we study ergodicity and mixing property of some measure preserving transformations on the Wiener space (W,H,\mu) which are generated by some random unitary operators defined on the Cameron-Martin space H.