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On SLE martingales in boundary WZW models
SLE martingales boundary WZW models
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2011/1/21
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}, 1
Subordination orthogonal martingales $L^{p}, 1
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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}, 1
Some new Bellman functions subordination orthogonal martingales
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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
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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...
Finitely additive equivalent martingale measures
Arbitrage de Finetti’s coherence principle equivalent martin-gale measure
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2011/1/21
Let L be a linear space of real bounded random variables on the probability space ( ,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L.
Rational term structure models with geometric Levy martingales
Rational term structure models geometric Levy martingales
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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.
Exactly solvable Schrödinger operators
Schrö dinger operators
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2010/11/29
We systematically describe and classify 1-dimensional Schr¨odinger equations that can be solved in terms of hypergeometric type functions. Beside the well-known families, we explicitly describe 2 new ...
Regularity and blow up for active scalars
Regularity blow up active scalars
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2010/11/29
We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equ...
A note on Mahler's conjecture
convex bodies volume product Mahler’s conjecture
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2010/12/8
Let K be a convex body in Rn with Santal´o point at 0. We show that if K has a point on the boundary with positive generalized Gauß curvature, then the volume product |K||K◦| is not ...
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
Non-equilibrium Markovian Process Fluctuation-Dissipation Theorems Fluctuation Relations Martingale
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2010/12/15
In the context of Markovian evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a ...
Characterizations of processes with stationary and independent increments under $G$-expectation
Characterizations of processes stationary independent increments
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2010/11/26
Our purpose is to investigate properties for processes with stationary and independent increments under G-expectation. As applications,we prove the martingale characterization to G-Brownian motion and...
On the speed of approach to equilibrium for a collisionless gas
Free-molecular gas Approach to equilibrium Diffuse reflection
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2010/12/7
We investigate the speed of approach to Maxwellian equilibrium for a collisionless gas enclosed in a vessel whose wall are kept at a uniform,constant temperature, assuming diffuse reflection of gas mo...
A thin-thick Decomposition for Hardy Martingales
Hardy Martingales Martingale Inequalities Complex Convexity
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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...
广义鞅变换算子的p-Amemiya范数不等式及其应用
鞅变换 p-Amemiya范数 p一致凸性 q一致光滑性
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2012/11/22
证明了一类广义鞅变换算子的p-Amemiya范数不等式.作为其应用又给出了证明B值鞅的极大函数与p阶均方函数的p-Amemiya范数不等式的一种新方法，其结果刻画了Banach空间的p一致凸性和q一致光滑性.