Theoretical Statistics and Mathematics Unit, ISI Delhi

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]

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