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On convergence in distribution of the Markov chain generated by the filter kernel induced by a fully dominated Hidden Markov Model

Seria
Rozprawy Matematyczne tom/nr w serii: 514 wydano: 2016
Zawartość
Warianty tytułu
Abstrakty
EN
Consider a Hidden Markov Model (HMM) such that both the state space and the observation space are complete, separable, metric spaces and for which both the transition probability function (tr.pr.f.) determining the hidden Markov chain of the HMM and the tr.pr.f. determining the observation sequence of the HMM have densities. Such HMMs are called fully dominated. In this paper we consider a subclass of fully dominated HMMs which we call regular.
A fully dominated, regular HMM induces a tr.pr.f. on the set of probability density functions on the state space which we call the filter kernel induced by the HMM and which can be interpreted as the Markov kernel associated to the sequence of conditional state distributions.
We show that if the underlying hidden Markov chain of the fully dominated, regular HMM is strongly ergodic and a certain coupling condition is fulfilled, then, in the limit, the distribution of the conditional distribution becomes independent of the initial distribution of the hidden Markov chain and, if also the hidden Markov chain is uniformly ergodic, then the distributions tend towards a limit distribution.
In the last part of the paper, we present some more explicit conditions, implying that the coupling condition mentioned above is satisfied.
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Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 514
Liczba stron
67
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2016
Twórcy
  • Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Bibliografia
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.bwnjournal-rm-doi-10_4064-dm739-9-2015
Identyfikatory
DOI
10.4064/dm739-9-2015
Kolekcja
DML-PL
Zawartość książki

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