巴拿赫空间上的通用广义函数和有限绝对连续度量

arXiv - MATH - Probability Pub Date : 2024-09-14 DOI:arxiv-2409.09303

A. A. Dorogovtsev, Naoufel Salhi

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引用次数: 0

摘要

在本文中，我们收集了随机过程的函数向这些过程的广义函数收敛的几个例子。我们注意到，就维纳度量而言，极限总是有限绝对连续的。我们试图用巴拿赫空间中概率度量的收敛来统一这些例子。关键概念是均匀有限绝对连续性条件。

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Universal generalized functionals and finitely absolutely continuous measures on Banach spaces

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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arXiv - MATH - Probability

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