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June, 1977 Every Nonnegative Submartingale is the Absolute Value of a Martingale
David Gilat
Ann. Probab. 5(3): 475-481 (June, 1977). DOI: 10.1214/aop/1176995809

Abstract

It is shown that every nonnegative superfair process (in particular a nonnegative submartingale) is the absolute value of a symmetric fair process (martingale). Is every submartingale a convex function of a martingale? No. If however the adjective convex is omitted from the question, an affirmative answer is provided. Furthermore, transforming functions $\phi$, such that every superfair process (submartingale) is that $\phi$ of a fair process (martingale), are shown to exist. The results are extended to continuous-parameter submartingales with rightcontinuous sample functions.

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David Gilat. "Every Nonnegative Submartingale is the Absolute Value of a Martingale." Ann. Probab. 5 (3) 475 - 481, June, 1977. https://doi.org/10.1214/aop/1176995809

Information

Published: June, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0364.60076
MathSciNet: MR433586
Digital Object Identifier: 10.1214/aop/1176995809

Subjects:
Primary: 60G45

Keywords: convex function , regular conditional distribution , strategy , submartingale , Superfair process

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 3 • June, 1977
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