Semi-Uniform Feller Stochastic Kernels

TL;DR

This paper introduces and analyzes semi-uniform Feller continuity for transition probabilities in Polish spaces, providing foundational results that support the theory of Markov decision processes with incomplete information.

Contribution

It defines and explores semi-uniform Feller continuity, including its equivalent characterizations and preservation under integration, advancing the mathematical framework for Markov decision processes.

Findings

Multiple equivalent definitions of semi-uniform Feller continuity

Proved preservation of this property under integration

Provides foundational results for Markov decision processes with incomplete information

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 fundamental results useful for this theory.