On weak feller continuity properties of non-linear filters

Name: On weak feller continuity properties of non-linear filters
Author: Kara, A. D., Saldı, Naci, Yuksel, S.

İsim	On weak feller continuity properties of non-linear filters
Yazar	Kara, A. D., Saldı, Naci, Yuksel, S.
Basım Tarihi:	2019
Basım Yeri	- IEEE
Tür	Belge
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	978-1-7281-1398-2
Kayıt Numarası	54726f71-5b07-435a-a6d1-04cffbf1176c
Lokasyon	Natural and Mathematical Sciences
Tarih	2019
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. 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

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Kaynağa git

On weak feller continuity properties of non-linear filters

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

Basım Tarihi 2019

Basım Yeri - IEEE

Tür Belge

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 978-1-7281-1398-2

Kayıt Numarası 54726f71-5b07-435a-a6d1-04cffbf1176c

Lokasyon Natural and Mathematical Sciences

Tarih 2019

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. 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