Martingale convergence via the square function-Reference-Cited by-同舟云学术

Martingale convergence via the square function

Published:1981 Issue:1 Volume:83 Page:125-127
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Chen Louis H. Y.

Abstract

By exploiting the natural setting of a convergence theorem of Burkholder, a direct and elementary proof of the theorem is given. This proof is also new for the martingale convergence theorem and the martingale transform convergence theorem which are corollaries to the above-mentioned convergence theorem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1981-083-01/S0002-9939-1981-0619996-6/S0002-9939-1981-0619996-6.pdf

Reference11 articles.

1. A sample function property of martingales;Austin, D. G.;Ann. Math. Statist.,1966

2. Another look at the martingale theorem;Báez-Duarte, Luis;J. Math. Anal. Appl.,1968

3. On the convergence of martingale transforms;Báez-Duarte, Luis;Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,1971

4. Martingale transforms;Burkholder, D. L.;Ann. Math. Statist.,1966

5. Distribution function inequalities for martingales;Burkholder, D. L.;Ann. Probability,1973

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