Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures

Abstract

Let E be an infinite-dimensional locally convex space, let { n } be a weakly convergent sequence of probability measures on E, and let {E n } be a sequence of Dirichlet forms on E such that E n is defined on L 2 ( n ). General sufficient conditions for Mosco convergence of the gradient Dirichlet forms are obtained. Applications to Gibbs states on a lattice and to the Gaussian case are given. Weak convergence of the associated processes is discussed.

Singular perturbations to semilinear stochastic heat equations

“…However, starting with the seminal works of Mosco [25,26], a number of authors have investigated sufficient conditions for the resolvent convergence of Dirichlet forms, see for example [2,3,21,24,28]. While our setting does not formally seem to be covered by these works, it 'morally' falls into the same category.…”

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

“…During the last decade one may have observed an increasing interest in Mosco convergence relative to Dirichlet forms with changing reference measures or, more general, on sequences of Hilbert spaces, see [5], [7], [8], [20], [23]. Most fundamental in this sense is [12].…”

Quasi regular Dirichlet forms and the stochastic quantization problem

“…For newer developments see also [AFHMR92], [Aid00], [Alb03], [ARü05], [ARW01], [Fu84], [DG97], [E99], [Ma95], [Kol06].…”