Author
Kara, A. D., Saldı, Naci, Yüksel, S.
Publication Date
2019-12
Publication Place
-
Elsevier
Subject
Non-linear filtering, Partially observed stochastic control
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0167-6911
Record ID
cfac1481-d3a1-43fa-9e7e-c6527b1e69e2
Library Location
Natural and Mathematical Sciences
Date
2019-12
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. Establishing sufficient conditions for the weak Feller property for such processes is a significant problem, studied under various assumptions and setups in the literature. 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
10.1016/j.sysconle.2019.104512
Cilt
134
