Semi-uniform Feller Stochastic Kernels

This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduces and studies the property of semi-uniform Feller continuity. This paper provides several equivalent definitions of semi...

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Veröffentlicht in:Journal of theoretical probability 2023-12, Vol.36 (4), p.2262-2283
Hauptverfasser: Feinberg, Eugene A., Kasyanov, Pavlo O., Zgurovsky, Michael Z.
Format: Artikel
Sprache:eng
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Zusammenfassung:This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduces and studies the property of semi-uniform Feller continuity. This paper provides several equivalent definitions of semi-uniform Feller continuity and establishes its preservation under integration. The motivation for this study came from the theory of Markov decision processes with incomplete information, and this paper provides the fundamental results useful for this theory.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-022-01230-9