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Estimating Gaps in Martingales and Applications to Coin-Tossing: Constructions and Hardness
information theory foundations distributed cryptography
2019/7/8
Consider the representative task of designing a distributed coin-tossing protocol for nn processors such that the probability of heads is X0∈[0,1]X0∈[0,1], and an adversary can reset one processor to ...
Approximating Martingales for Variance Reduction in Markov Process Simulation
Variance reduction Markov process simulation martingale
2015/7/8
“Knowledge of either analytical or numerical approximations should enable more efficient simulation estimators to be constructed.” This principle seems intuitively plausible and certainly attractive, ...
Parabolic martingales and non-symmetric Fourier multipliers
Parabolic martingales non-symmetric Fourier multipliers Functional Analysis
2012/6/18
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...
A Representation Theorem for Smooth Brownian Martingales
Continuous Martingales Malliavin Calculus Probabilistic Methods for Partial Differential Equations
2012/5/24
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...
PAC-Bayesian Analysis of Martingales and Multiarmed Bandits
PAC-Bayesian Analysis Martingales Multiarmed Bandits
2011/6/21
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent
random variables. The first is based on a new lemma that enables to bound expectations
of convex functions of...
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...
Uniqueness of the representation for $G$-martingales with finite variation
niqueness representation theorem G-martingale finite variation G-expectation
2011/1/19
Our purpose is to prove the uniqueness of the representation for G-martingales with finite variation.
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.
Subordination by orthogonal martingales in $L^{p}$ and zeros of Laguerre polynomials
orthogonal martingales $L^{p}$ zeros of Laguerre polynomials
2011/1/18
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 ...
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...
History of applications of martingales in survival analysis
History applications martingales survival analysis
2010/3/11
The paper traces the development of the use of martingale methods
in survival analysis from the mid 1970’s to the early 1990’s. This
development was initiated by Aalen’s Berkeley PhD-thesis in 1975,...
On convergence of L(1)-bounded martingales indexed by directed sets
convergence of L(1)-bounded martingales directed sets
2009/9/24
On convergence of L(1)-bounded martingales indexed by directed sets。