Description

• Title:
  Probability on submetric spaces
• Creator:
  Jakubowski, Adam
• Description:
  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”.
• Object availability:
  free access
• Date:
  2023.07.26
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol. 37 No. 2 (2023); 138-148;
  Annales Mathematicae Silesianae; Tom 37 Nr 2 (2023); 138-148;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/15792/12180
• Subject:
  submetric space;
  sequential topologies;
  convergence of probability measures;
  convergence in probability;
  Skorokhod almost sure representation;
  stochastic compactness method
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/15792
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other