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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On modification theorems
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by Murali Rao PDF
Trans. Amer. Math. Soc. 167 (1972), 443-450 Request permission

Abstract:

Given a right continuous family ${F_t}$ of complete $\sigma$-fields and a bounded right continuous family ${X_t}$ of random variables, we show in this paper that it is possible to modify the conditional expectations $E({X_t}|{F_t})$ to be right continuous. When ${X_t} = X$, this reduces to a result of J. L. Doob.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 167 (1972), 443-450
  • MSC: Primary 60G45
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0362478-9
  • MathSciNet review: 0362478