Tightness and weak convergence of probabilities on the Skorokhod space on the dual of a nuclear space and applications

Abstract

Let $\Phi ’_{\beta }$ denote the strong dual of a nuclear space $\Phi $ and let $D_{T}(\Phi ’_{\beta })$ be the Skorokhod space of right-continuous with left limits (càdlàg) functions from $[0,T]$ into $\Phi ’_{\beta }$. We introduce the concepts of