Semi-uniform Feller Stochastic Kernels

Eugene A. Feinberg (), Pavlo O. Kasyanov () and Michael Z. Zgurovsky ()
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Eugene A. Feinberg: Stony Brook University
Pavlo O. Kasyanov: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
Michael Z. Zgurovsky: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

Journal of Theoretical Probability, 2023, vol. 36, issue 4, 2262-2283

Abstract: Abstract 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.

Keywords: Stochastic kernel; Semi-uniform Feller; Weak convergence; Convergence in total variation; Borel set; Primary 60B10; Secondary 60J05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01230-9

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