Computable infinite-dimensional filters with applications to discretized diffusion processes

Mireille Chaleyat-Maurel and Valentine Genon-Catalot

Stochastic Processes and their Applications, 2006, vol. 116, issue 10, 1447-1467

Abstract: Let us consider a pair signal-observation ((xn,yn),n>=0) where the unobserved signal (xn) is a Markov chain and the observed component is such that, given the whole sequence (xn), the random variables (yn) are independent and the conditional distribution of yn only depends on the corresponding state variable xn. The main problems raised by these observations are the prediction and filtering of (xn). We introduce sufficient conditions allowing us to obtain computable filters using mixtures of distributions. The filter system may be finite or infinite-dimensional. The method is applied to the case where the signal xn=Xn[Delta] is a discrete sampling of a one-dimensional diffusion process: Concrete models are proved to fit in our conditions. Moreover, for these models, exact likelihood inference based on the observation (y0,...,yn) is feasible.

Keywords: Stochastic; filtering; Diffusion; processes; Discrete; time; observations; Hidden; Markov; models; Prior; and; posterior; distributions (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00030-5
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:116:y:2006:i:10:p:1447-1467

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().