Submitted Paper

Inserted: 10 jan 2025
Last Updated: 10 jan 2025

Journal: SN Partial Differential Equations and Applications
Year: 2025

Abstract:

The study of stochastic processes in both vector spaces and manifolds is essential across numerous fields of Mathematics, Physics, and Applied Sciences. Altough significant research exists on infinite-dimensional vector spaces and finite-dimensional manifolds, the study of processes in infinite-dimensional manifolds is less developed. One key distinction in this setting is that infinite-dimensional manifolds are not locally compact, necessitating revisions to techniques commonly used in finite dimensions. % This compendium gathers a comprehensive collection of results and examples—some widely known, others potentially novel—aimed at those interested in the field. These findings have been used in the paper \textit{Tightness of Random Walks in Infinite Dimensional Spaces and Manifolds}, but may provide a useful reference for further exploration of these subjects.

Keywords: Tightness, Stochastic processes, infinite dimensional manifolds, nets

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