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A Ratio Limit Theorem for Approximate Martingales

Published online by Cambridge University Press:  20 November 2018

Charles W. Lamb
Charles W. Lamb*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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It has been proved [3, p. 630] that the martingale convergence theorem obtained by Andersen and Jessen [1, p. 5] follows from the classical theory developed by Doob. By using some results of Yosida and Hewitt [9] on finitely additive set functions, Johansen and Karush [7] proved that the identification of the limit function as a derivative in the approach of Andersen and Jessen can be obtained in the general case. In this paper we sharpen the methods of Andersen and Jessen to obtain a ratio limit theorem for “approximate martingales”.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 772 - 779
Copyright
Copyright © Canadian Mathematical Society 1973

References

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