# Publications and Preprints

On characterisation of Markov processes via martingale problems
by
Abhay G. Bhatt, Rajeeva L. Karandikar and B. V. Rao
It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions implies measurability of the transition probability functions and hence Markovian property of the solution. 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 an example of a martingale problem that is well posed in the class of solutions which are continuous in probability but for which no r.c.l.l. solution exists.

isid/ms/2003/19 [fulltext]