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We show that, under certain smoothness conditions, a Brownian martingale at a fixed time can be represented as an exponential of its value at a later time. The time-dependent generator of this exponen...
Following [3], we consider the boundary WZW model on a half–plane with a cut growing according to the Schramm–Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and a...
The main result of this note is Theorem 7 below. The main interest is the array of new Bellman function, very different from Burkholder’s function.
The two mathematicians who have most advanced martingale theory in the last seventy years are Joseph Doob and Donald Burkholder. Martingales as a remarkably flexible tool are used throughout probabili...
In the \positive interest" models of Flesaker and Hughston, the nominal discount bond system is determined by the speci cation of a one-parameter family of positive martingales.
We prove thin-thick decompositions, for the class of Hardy martingales and thereby strenghten its square function characterization. We apply the underlying method to several classical martinale inequa...

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