The Annals of Probability

Martingales with a Countable Filtering Index Set

J.-P. Gabriel

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Abstract

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.

Article information

Source
Ann. Probab., Volume 5, Number 6 (1977), 888-898.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995658

Digital Object Identifier
doi:10.1214/aop/1176995658

Mathematical Reviews number (MathSciNet)
MR445603

Zentralblatt MATH identifier
0432.60055

JSTOR
links.jstor.org

Subjects
Primary: 60G45
Secondary: 60F15: Strong theorems 60G50: Sums of independent random variables; random walks

Keywords
Filtering sets martingales almost everywhere convergence law of large numbers sectors stochastic convexity

Citation

Gabriel, J.-P. Martingales with a Countable Filtering Index Set. Ann. Probab. 5 (1977), no. 6, 888--898. doi:10.1214/aop/1176995658. https://projecteuclid.org/euclid.aop/1176995658


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