Donsker's invariance principle is shown to hold for random walks in rough path topology. As application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.

Abstract. In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not converge to any deterministic distribution, they do have a weak weak limit in the sense that viewed as random elements of the space of probability measur...

We will extend the main result of [1] to non-unital case with a totally different proof. More precisely, we give an abstract characterization arbitrary self-adjoint weak⁎-closed subspace L(H) (equipped induced matrix norm, cone and weak⁎-topology). In order do this, analogue Bonsall for ⁎-operator spaces equipped closed cones.

This document is a summary of basic facts about the “standard” category of compactly generated spaces introduced by McCord [McC69] (often referred to in the literature as “compactly generated weak Hausdorff spaces”, or “weak Hausdorff k-spaces”). The main references I’ve used for this material are Gaunce Lewis’s thesis [Lew, App. A], and Neil Strickland’s note [Str09] (especially for material a...

We prove that the weakly damped nonlinear Schrödinger flow in L 2 (R) provides a dynamical system which possesses a global attractor. The proof relies on the continuity of the Schrödinger flow for the weak topology in L 2 (R).

We characterize the relaxation of the perimeter in an infinite dimensional Wiener space, with respect to the weak L-topology. We also show that the rescaled AllenCahn functionals approximate this relaxed functional in the sense of Γ-convergence.

We present a proof of Sklar’s Theorem that uses topological arguments, namely compactness (under the weak topology) of the class of copulas and some density properties of the class of distribution functions.