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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...
Subordination by orthogonal martingales in $L^{p}, 1le 2$
Subordination orthogonal martingales $L^{p}, 1
2011/1/18
We are given two martingales on the filtration of the two dimensional Brownian motion. One is subordinated to another. We want to give an estimate of Lp-norm of a subordinated one via the same norm of...
Some new Bellman functions and subordination by orthogonal martingales in $L^{p}, 1le 2$
Some new Bellman functions subordination orthogonal martingales
2011/1/18
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.
Donald Burkholder's work in martingales and analysis
Donald Burkholder's work martingales analysis
2011/2/24
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...
Rational term structure models with geometric Levy martingales
Rational term structure models geometric Levy martingales
2011/3/2
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.
A thin-thick Decomposition for Hardy Martingales
Hardy Martingales Martingale Inequalities Complex Convexity
2010/12/8
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...