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Proceedings of the American Mathematical Society

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Positive martingales and their induced measures


Authors: Bennett Eisenberg and Shi Xin Gan
Journal: Proc. Amer. Math. Soc. 89 (1983), 680-684
MSC: Primary 60G30
DOI: https://doi.org/10.1090/S0002-9939-1983-0718996-7
MathSciNet review: 718996
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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.


References [Enhancements On Off] (What's this?)

  • [1972] Robert B. Ash, Real analysis and probability, Academic Press, New York-London, 1972. Probability and Mathematical Statistics, No. 11. MR 0435320
  • [1977] 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.
  • [1975] J. 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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0718996-7
Article copyright: © Copyright 1983 American Mathematical Society