• Rajeeva L Karandikar

      Articles written in Proceedings – Mathematical Sciences

    • Measure free martingales

      Rajeeva L Karandikar M G Nadkarni

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      We give a necessary and sufficient condition on a sequence of functions on a set Ω under which there is a measure on Ω which renders the given sequence of functions a martingale. Further such a measure is unique if we impose a natural maximum entropy condition on the conditional probabilities.

    • On characterisation of Markov processes via martingale problems

      Abhay G Bhatt Rajeeva L Karandikar B V Rao

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      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.

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