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Martingale Problems for Conditional Distributions of Markov Processes

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1.	Title	Title of document	Martingale Problems for Conditional Distributions of Markov Processes
2.	Creator	Author's name, affiliation, country	Thomas G. Kurtz; University of Wisconsin, Madison
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	partial observation, conditional distribution, filtering, forward equation, martingale problem, Markov process, Markov function, quasireversibility, measure-valued process
3.	Subject	Subject classification	60G35, 69J25, 60J35, 93E11, 60G09, 60G44
4.	Description	Abstract	Let $X$ be a Markov process with generator $A$ and let $Y(t)=\gamma (X(t))$. The conditional distribution $\pi_t$ of $X(t)$ given $\sigma (Y(s):s\leq t)$ is characterized as a solution of a filtered martingale problem. As a consequence, we obtain a generator/martingale problem version of a result of Rogers and Pitman on Markov functions. Applications include uniqueness of filtering equations, exchangeability of the state distribution of vector-valued processes, verification of quasireversibility, and uniqueness for martingale problems for measure-valued processes. New results on the uniqueness of forward equations, needed in the proof of uniqueness for the filtered martingale problem are also presented.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1998-07-06
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/31
10.	Identifier	Digital Object Identifier	10.1214/EJP.v3-31
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 3
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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