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1998 Martingale Problems for Conditional Distributions of Markov Processes
Thomas Kurtz
Author Affiliations +
Electron. J. Probab. 3: 1-29 (1998). DOI: 10.1214/EJP.v3-31


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.


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Thomas Kurtz. "Martingale Problems for Conditional Distributions of Markov Processes." Electron. J. Probab. 3 1 - 29, 1998.


Accepted: 6 July 1998; Published: 1998
First available in Project Euclid: 29 January 2016

zbMATH: 0907.60065
MathSciNet: MR1637085
Digital Object Identifier: 10.1214/EJP.v3-31

Primary: 60G35
Secondary: 60G09 , 60G44 , 60J35 , 69J25 , 93E11

Keywords: conditional distribution , Filtering , forward equation , Markov function , Markov process , Martingale problem , Measure-valued process , partial observation , quasireversibility

Vol.3 • 1998
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