Weak Feller property of non-linear filters

Name: Weak Feller property of non-linear filters
Author: Kara, A. D., Saldı, Naci, Yüksel, S.

İsim	Weak Feller property of non-linear filters
Yazar	Kara, A. D., Saldı, Naci, Yüksel, S.
Basım Tarihi:	2019-12
Basım Yeri	- Elsevier
Konu	Non-linear filtering, Partially observed stochastic control
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0167-6911
Kayıt Numarası	cfac1481-d3a1-43fa-9e7e-c6527b1e69e2
Lokasyon	Natural and Mathematical Sciences
Tarih	2019-12
Notlar	Natural Sciences and Engineering Research Council of Canada
Örnek Metin	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

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Kaynağa git

Weak Feller property of non-linear filters

Yazar Kara, A. D., Saldı, Naci, Yüksel, S.

Basım Tarihi 2019-12

Basım Yeri - Elsevier

Konu Non-linear filtering, Partially observed stochastic control

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0167-6911

Kayıt Numarası cfac1481-d3a1-43fa-9e7e-c6527b1e69e2

Lokasyon Natural and Mathematical Sciences

Tarih 2019-12

Notlar Natural Sciences and Engineering Research Council of Canada

Örnek Metin 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