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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/116/01/0083-0096

    • Keywords

       

      Martingale problem; Markov processes; semigroup; path properties

    • 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.

    • Author Affiliations

       

      Abhay G Bhatt1 Rajeeva L Karandikar1 B V Rao1 2

      1. Indian Statistical Institute, 7, SJS Sansanwal Marg, New Delhi - 110 016, India
      2. Indian Statistical Institute, 203, B.T. Road, Kolkata - 700 108, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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