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XIII: 58, 642-645, LNM 721 (1979)

**MAISONNEUVE, Bernard**

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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XIV: 07, 62-75, LNM 784 (1980)

**BARLOW, Martin T.**; **YOR, Marc**

Sur la construction d'une martingale continue de valeur absolue donnée (Martingale theory)

This paper consists of two notes on Gilat's theorem (*Ann. Prob.* **5**, 1977, See also 1358). The problem consists in constructing, given a continuous positive submartingale $Y$, a *continuous * martingale $X$ (possibly on a different space) such that $|X|$ has the same law as $Y$. Let $A$ be the increasing process associated with $Y$; it is necessary for the existence of $X$ that $dA$ should be carried by $\{Y=0\}$. This is shown by the first note (Yor's) to be also sufficient---more precisely, in this case the solutions of Gilat's problem are all continuous. The second note (Barlow's) shows how to construct a Gilat martingale by ``putting a random $\pm$ sign in front of each excursion of $Y$'', a simple intuitive idea and a delicate proof

Keywords: Gilat's theorem

Nature: Original

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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 (

Comment: See also 1407

Keywords: Gilat's theorem

Nature: Exposition, Original additions

Retrieve article from Numdam

XIV: 07, 62-75, LNM 784 (1980)

Sur la construction d'une martingale continue de valeur absolue donnée (Martingale theory)

This paper consists of two notes on Gilat's theorem (

Keywords: Gilat's theorem

Nature: Original

Retrieve article from Numdam