2003, Volume 65, Pt. 4 , 733--743

MARTINGALE  PROBLEMS AND PATH PROPERTIES OF SOLUTIONS

By

ABHAY G. BHATT and RAJEEVA L. KARANDIKAR, Indian Statistical Institute, New Delhi, India

SUMMARY. Existence and uniqueness of solutions to martingale problems, not only in the class of r.c.l.l. or continuous process, but also in the class of progressively measurable processes   has become important. In this article we give several examples which show that existence or uniqueness in any one class need not imply the same in another class. We also give an example of a well-posed martingale problem where the operator is not a core for the generator of the corresponding Markov process.

AMS (1991) subject classification. Primary 60J25; secondary 60G17, 60J35.

Key words and phrases. Martingale problems, path properties, generator, core.

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