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XIII: 58, 642-645, LNM 721 (1979)
Martingales de valeur absolue donnée, d'après Protter-Sharpe (Martingale theory)
The main difficulty of Gilat's theorem (every positive submartingale $X$ can be interpreted as the absolute value of a martingale, in a suitably enlarged filtration) is due to the zeros of $X$. In the strictly positive case a simple proof was given by Protter and Sharpe (Ann. Prob., 7, 1979). This proof is further simplified and slightly generalized
Comment: See also 1407
Keywords: Gilat's theorem
Nature: Exposition, Original additions
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