Probability on Submetric Spaces

• Autorzy: Adam Jakubowski
• Języki publikacji: EN

Abstrakty

EN

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". (original abstract)

Słowa kluczowe

EN

Stochastic processes; Probability theory; Differential equations

PL

Procesy stochastyczne; Teoria prawdopodobieństwa; Równania różniczkowe

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2023
• Tom: 37 (2)
• Strony: 138--148

Twórcy

autor

Adam Jakubowski

• Nicolaus Copernicus University in Toruń, Poland

Bibliografia

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Identyfikatory

DOI

10.2478/amsil-2023-0012