## Electronic Journal of Probability

### Martingale Problems for Conditional Distributions of Markov Processes

Thomas Kurtz

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 3 (1998), paper no. 9, 29 pp.

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

https://projecteuclid.org/euclid.ejp/1454101769

Digital Object Identifier
doi:10.1214/EJP.v3-31

Mathematical Reviews number (MathSciNet)
MR1637085

Zentralblatt MATH identifier
0907.60065

Rights

#### Citation

Kurtz, Thomas. Martingale Problems for Conditional Distributions of Markov Processes. Electron. J. Probab. 3 (1998), paper no. 9, 29 pp. doi:10.1214/EJP.v3-31. https://projecteuclid.org/euclid.ejp/1454101769

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