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We give a class of Fourier multipliers with non-symmetric symbols and explicit norm bounds on $L^p$ spaces by using the stochastic calculus of L\'evy processes and Burkholder-Wang estimates for differ...
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...
Our purpose is to prove the uniqueness of the representation for G-martingales with finite variation.
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.
In this paper we address the question of finding the best Lp-norm constant for martingale transforms with one-sided orthogonality. Let O = (,B, P)be a probability space with filtration B generated by ...
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...
We study maximal inequalities for demisubmartingales and N-demisupermartingales and obtain inequalities between dominated demisubmartingales. A sequence of partial sums of zero mean associated random ...
In this paper, we prove that the process of product variation of a two-parameter smooth martingale admits an $\infty$ modification, which can be constructed as the quasi-sure limit of sum of the corre...

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