Universal generalized functionals and finitely absolutely continuous measures on Banach spaces

2024/09/14 by A. A. Dorogovtsev, Dorogovtsev, A. A., Naoufel Salhi +1
Mathematics · #Mathematical and Theoretical Analysis #Advanced Banach Space Theory #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2409.09303

Abstract

In this paper we collect several examples of convergence of functions of random processes to generalized functionals of those processes. We remark that the limit is always finitely absolutely continuous with respect to Wiener measure. We try to unify those examples in terms of convergence of probability measures in Banach spaces. The key notion is the condition of uniform finite absolute continuity.

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