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Martingale Problems for Conditional Distributions of Markov Processes

   
@article{EJP31,
	author = {Thomas Kurtz},
	title = {Martingale Problems for Conditional Distributions of Markov Processes},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {3},
	year = {1998},
	keywords = {partial observation, conditional distribution, filtering, forward equation, martingale problem, Markov process, Markov function, quasireversibility, measure-valued process},
	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.},
	pages = {no. 9, 1-29},
	issn = {1083-6489},
	doi = {10.1214/EJP.v3-31},    
        url = {http://ejp.ejpecp.org/article/view/31}}