## EVENT DETAILS AND ABSTRACT

**Analysis and Probability Seminar**
**Title:** Quasi-invariant Measures on Path Space

**Speaker:** Professor Denis Bell

**Speaker Info:** University of North Florida

**Brief Description:**

**Special Note**:

**Abstract:**

Let *N* denote a manifold equipped with a finite Borel measure γ. A vector field *Z* on *N* is said to be admissible with respect to γ
if *Z* admits an integration by parts formula. The measure γ is said to be quasi-invariant under *Z*
if the class of null sets of γ is preserved by the flow generated by *Z*. In this talk we study the law γ of an elliptic
diffusion process with values in a closed compact manifold. We construct a class of admissible vector fields for γ, show that γ
is quasi-invariant under these vector fields, and give a formula for the associated family of Radon-Nikodym derivatives *dγ*_{s}/dγ.
This work provides an alternative approach to the Cameron-Martin theorem for Wiener measure on a manifold proved by Driver in 1992.

**Date:** Monday, April 30, 2007

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Elton P. Hsu

**Contact email:** elton@math.northwestern.edu

**Contact Phone:** 847-491-8541

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