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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive martingales and their induced measures
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by Bennett Eisenberg and Shi Xin Gan PDF
Proc. Amer. Math. Soc. 89 (1983), 680-684 Request permission

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
  • Robert B. Ash, Real analysis and probability, Probability and Mathematical Statistics, No. 11, Academic Press, New York-London, 1972. 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.
  • J. Neveu, Discrete-parameter martingales, Revised edition, North-Holland Mathematical Library, Vol. 10, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. Translated from the French by T. P. Speed. MR 0402915
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • 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