EVENT DETAILS AND ABSTRACT

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.