Probability on Submetric Spaces

Adam Jakubowski

doi:10.2478/amsil-2023-0012

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Probability on Submetric Spaces

Annales Mathematicae Silesianae

Volume 37 (2023): Issue 2 (September 2023)

By: Adam Jakubowski

Open Access

|Jul 2023

Abstract

A submetric space is a topological space with continuous metrics, generating a metric topology weaker than the original one (e.g. a separable Hilbert space with the weak topology).

We demonstrate that on submetric spaces there exists a theory of convergence in probability, in law etc. equally effective as the Probability Theory on metric spaces. In the theory on submetric spaces the central role is played by a version of the Skorokhod almost sure representation, proved by the author some 25 years ago and in 2010 rediscovered by specialists in stochastic partial differential equations in the form of “stochastic compactness method”.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2023-0012 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 138 - 148

Submitted on: Jan 25, 2023

Accepted on: Jul 13, 2023

Published on: Jul 26, 2023

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

submetric space,

sequential topologies,

convergence of probability measures,

convergence in probability,

Skorokhod almost sure representation,

stochastic compactness method

Related subjects:

Mathematics,

General mathematics

© 2023 Adam Jakubowski, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 37 (2023): Issue 2 (September 2023)