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Shorter Notes: A Short Proof of the Martingale Convergence Theorem
Charles W. Lamb
Proceedings of the American Mathematical Society
Vol. 38, No. 1 (Mar., 1973), pp. 215-217
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2038800
Page Count: 3
You can always find the topics here!Topics: Martingales, Mathematical theorems, Perceptron convergence procedure, Mathematical inequalities
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The martingale convergence theorem is first proved for uniformly integrable martingales by a standard application of Doob's maximal inequality. A simple truncation argument is then given which reduces the proof of the L1-bounded martingale theorem to the uniformly integrable case. A simple method is used to prove Burkholder's martingale transform convergence theorem.
Proceedings of the American Mathematical Society © 1973 American Mathematical Society