Rotations and Tangent Processes on Wiener Space

Abstract

The paper considers (a) Representations of measure preserving transformations (``rotations'') on Wiener space, and (b) The stochastic calculus of variations induced by parameterized rotations $\{T_θw, 0 \le θ\le \eps\}$: ``Directional derivatives'' $(dF(T_{\theta }w)/d\theta {)}_{\theta =0}$, ``vector fields'' or ``tangent processes'' $(d{T}_{\theta }w/d\theta {)}_{\theta =0}$ and flows of rotations.

29 pages