Author
Kara, A. D., Saldı, Naci, Yuksel, S.
Publication Date
2019
Publication Place
-
IEEE
Type
Document
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
978-1-7281-1398-2
Record ID
54726f71-5b07-435a-a6d1-04cffbf1176c
Library Location
Natural and Mathematical Sciences
Date
2019
Notes
Natural Sciences and Engineering Research Council of Canada
Sample Text
Weak Feller property of controlled and control free Markov chains leads to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability of numerical approximation methods. For controlled setups, this leads to existence and approximation results for optimal control policies. We know from stochastic control theory that partially observed systems can be converted to fully observed systems by replacing the original state space with a probability measure-valued state space, with the corresponding kernel acting on probability measures known as the non-linear filter process. In this paper, we prove the weak Feller property of the non-linear filter process (i) first under weak continuity of the transition probability of controlled Markov chain and total variation continuity of its observation channel, and then, (ii) under total variation continuity of the transition probability of controlled Markov chain. The former result (i) has first appeared in Feinberg et. al. (2016). Here, we present a concise and easy to follow alternative proof for this existing result. The latter result (ii) establishes weak Feller property of non-linear filter process under conditions which have not been previously reported in the literature.
DOI
10.1109/CDC40024.2019.9030100
