Mosco Type Convergence and Weak Convergence for a Fleming-Viot type Particle System

Abstract

We are concerned with Mosco type convergence for a non-symmetric n-particle Fleming-Viot system {X 1 , . . . , X n } in a bounded d-dimensional domain D with smooth boundary. Moreover, we are interested in relative compactness of the n-particle processes. It turns out that integration by parts relative to the initial measure and the generator is the appropriate mathematical tool. For finitely many particles, such integration by parts is established by using probabilistic arguments. For the limiting infinite dimensional configuration we use a result from infinite dimensional non-gaussian calculus.

Quasi-Invariance under Flows Generated by Non-Linear PDEs

“…The present article is the second in a series of three, see [16] and [17]. These papers are dedicated to Mosco-type convergence and weak convergence of particle systems.…”