On characterisation of Markov processes via martingale problems

Details On characterisation of Markov processes via martingale problems On characterisation of Markov processes via martingale problems

2006-07-25

arxiv.org/abs/math/0607613v1

Mathematics

Probability

14 pages

Scientific paper

It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale problem is well-posed in the class of solutions which are continuous in probability. This extension is used to improve on a criterion for a probability measure to be invariant for the semigroup associated with the Markov process. We also give examples of martingale problems that are well-posed in the class of solutions which are continuous in probability but for which no r.c.l.l. solution exists.

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