English

On characterisation of Markov processes via martingale problems

Probability 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0607613,
  title  = {On characterisation of Markov processes via martingale problems},
  author = {Abhay G Bhatt and Rajeeva L Karandikar and B V Rao},
  journal= {arXiv preprint arXiv:math/0607613},
  year   = {2007}
}

Comments

14 pages

R2 v1 2026-07-22T17:39:31.509Z