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Transactions of the American Mathematical Society

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



On modification theorems

Author: Murali Rao
Journal: Trans. Amer. Math. Soc. 167 (1972), 443-450
MSC: Primary 60G45
MathSciNet review: 0362478
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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}\vert{F_t})$ to be right continuous. When $ {X_t} = X$, this reduces to a result of J. L. Doob.

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

  • [1] Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0205288
  • [2] S. D. Chatterji, Martingale convergence and the Radon-Nikodym theorem in Banach spaces., Math. Scand. 22 (1968), 21–41. MR 0246341

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Keywords: Stochastic process, conditional expectation, modification, stopping times, super martingales
Article copyright: © Copyright 1972 American Mathematical Society