On Characterisation of Markov Processes Via Martingale Problems

Proceedings Mathematical Sciences

Rajeeva L Karandikar²  Abhay G Bhatt³  B V Rao¹ 

[1] $$;Indian Statistical Institute, 0, B.T. Road, Kolkata 00 0, India$$;Indian Statistical Institute, , SJS Sansanwal Marg, New Delhi 0 0, India$$

关键词: Martingale problem;    Markov processes;    semigroup;    path properties.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown