Positive martingales and their induced measures
Bennett Eisenberg and Shi Xin Gan
Proc. Amer. Math. Soc. 89 (1983), 680-684
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Abstract: Conditions for the absolute continuity of probability measures are given in terms of limits of sequences of Radon-Nikodym derivatives. In the other direction, conditions for the optional stopping theorem for positive martingales are given in terms of properties of their induced measures.
B. Ash, Real analysis and probability, Academic Press, New
York-London, 1972. Probability and Mathematical Statistics, No. 11. MR 0435320
J. M. Kabanov, R. S. Lipcer and A. N. Shiryaev, On the question of absolute continuity and singularity of probability measures, Math. USSR Sb. 33, 203-221.
Neveu, Discrete-parameter martingales, Revised edition,
North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier
Publishing Co., Inc., New York, 1975. Translated from the French by T. P.
Speed; North-Holland Mathematical Library, Vol. 10. MR 0402915
- Robert B. Ash, Real analysis and probability, Academic Press, New York. MR 0435320 (55:8280)
- J. M. Kabanov, R. S. Lipcer and A. N. Shiryaev, On the question of absolute continuity and singularity of probability measures, Math. USSR Sb. 33, 203-221.
- J. Neveu, Discrete parameter martingales, North-Holland, Amsterdam. MR 0402915 (53:6729)
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