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December, 1977 Martingales with a Countable Filtering Index Set
J.-P. Gabriel
Ann. Probab. 5(6): 888-898 (December, 1977). DOI: 10.1214/aop/1176995658


This paper is concerned with the almost everywhere convergence of martingales indexed by countable filtering sets. It is shown that the convergence is a consequence of the maximal inequality as it is in the classical case. It also contains some results about the law of large numbers when the index belongs to a sector and an optimal condition assuring the almost everywhere convergence of martingales in these sectors.


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J.-P. Gabriel. "Martingales with a Countable Filtering Index Set." Ann. Probab. 5 (6) 888 - 898, December, 1977.


Published: December, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0432.60055
MathSciNet: MR445603
Digital Object Identifier: 10.1214/aop/1176995658

Primary: 60G45
Secondary: 60F15 , 60G50

Keywords: Almost everywhere convergence , Filtering sets , Law of Large Numbers , Martingales , sectors , stochastic convexity

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • December, 1977
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