Universal generalized functionals and finitely absolutely continuous measures on Banach spaces

A. A. Dorogovtsev; Naoufel Salhi

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arXiv · 2409.09303

Universal generalized functionals and finitely absolutely continuous measures on Banach spaces

A. A. Dorogovtsev·Naoufel Salhi

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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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BibTeX RIS

A. A. Dorogovtsev, Naoufel Salhi. 2024-09-14. Universal generalized functionals and finitely absolutely continuous measures on Banach spaces. https://arxiv.org/abs/2409.09303

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