Mosco Type Convergence of Bilinear Forms and Weak Convergence of $n$-Particle Systems

Abstract

It is well known that Mosco (type) convergence is a tool in order to verify weak convergence of finite dimensional distributions of sequences of stochastic processes. In the present paper we are concerned with the concept of Mosco type convergence for non-symmetric stochastic processes and, in particular, n-particle systems in order to establish relative compactness.

Weak Convergence of $n$-Particle Systems Using Bilinear Forms

“…Under additional conditions weak convergence of stationary n-particle processes to stationary deterministic paths is proved. The method is applied to the particle approximation of a Ginzburg-Landau type diffusion.The present paper is in close relation to the paper [9]. Different definitions of bilinear forms and versions of Mosco type convergence are introduced.…”

“…The present paper is in close relation to the paper [9]. Different definitions of bilinear forms and versions of Mosco type convergence are introduced.…”

“…It is more general than what is used in order to establish relative compactness and weak convergence of particle systems in Subsection 3.4 and in Section 4. It prepares the calculus developed in Section 2 of [9] and it is appropriate in order to show weak convergence of invariant measures in Subsections 3.3 and 4.1 of the present paper.…”

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.…”