A strong law of large numbers for martingales
Authors:
Shey Shiung Sheu and Yu Shan Yao
Journal:
Proc. Amer. Math. Soc. 92 (1984), 283-287
MSC:
Primary 60G42; Secondary 60F15
DOI:
https://doi.org/10.1090/S0002-9939-1984-0754722-4
MathSciNet review:
754722
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Abstract | References | Similar Articles | Additional Information
Abstract: We derive a moment inequality for the Skorohod representation theorem and apply it to obtain a strong law of large numbers for martingales.
- Leo Breiman, On the tail behavior of sums of independent random variables, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 (1967), 20–25. MR 226707, DOI https://doi.org/10.1007/BF00535464
- Y. S. Chow, On a strong law of large numbers for martingales, Ann. Math. Statist. 38 (1967), 610. MR 208648, DOI https://doi.org/10.1214/aoms/1177698981
- David Freedman, Brownian motion and diffusion, Holden-Day, San Francisco, Calif.-Cambridge-Amsterdam, 1971. MR 0297016
- P. Hall and C. C. Heyde, Martingale limit theory and its application, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. Probability and Mathematical Statistics. MR 624435
- A. V. Skorohod, Issledovaniya po teorii sluchaĭ nykh protsessov (Stokhasticheskie differentsial′nye uravneniya i predel′nye teoremy dlya protsessov Markova), Izdat. Kiev. Univ., Kiev, 1961 (Russian). MR 0185619
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Additional Information
Keywords:
Brownian motion,
Skorohod’s representation,
strong law of large numbers,
martingale
Article copyright:
© Copyright 1984
American Mathematical Society
