The Experts below are selected from a list of 21 Experts worldwide ranked by ideXlab platform
Marek Biskup - One of the best experts on this subject based on the ideXlab platform.
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quenched invariance principle for simple random walk on percolation clusters
Probability Theory and Related Fields, 2006Co-Authors: N Berger, Marek BiskupAbstract:We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in ℤ d with d≥2. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a Square-Integrable Martingale. The size of the deformation, expressed by the so called corrector, is estimated by means of ergodicity arguments.
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quenched invariance principle for simple random walk on percolation clusters
arXiv: Probability, 2005Co-Authors: N Berger, Marek BiskupAbstract:We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in $\Z^d$ with $d\ge2$. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a Square-Integrable Martingale. The size of the deformation, expressed by the so called corrector, is estimated by means of ergodicity arguments.
N Berger - One of the best experts on this subject based on the ideXlab platform.
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quenched invariance principle for simple random walk on percolation clusters
Probability Theory and Related Fields, 2006Co-Authors: N Berger, Marek BiskupAbstract:We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in ℤ d with d≥2. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a Square-Integrable Martingale. The size of the deformation, expressed by the so called corrector, is estimated by means of ergodicity arguments.
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quenched invariance principle for simple random walk on percolation clusters
arXiv: Probability, 2005Co-Authors: N Berger, Marek BiskupAbstract:We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in $\Z^d$ with $d\ge2$. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a Square-Integrable Martingale. The size of the deformation, expressed by the so called corrector, is estimated by means of ergodicity arguments.
Shiqing Zheng - One of the best experts on this subject based on the ideXlab platform.
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set valued stochastic equation with set valued Square Integrable Martingale
ITM Web of Conferences, 2017Co-Authors: Shiqing ZhengAbstract:In this paper, we shall introduce the stochastic integral of a stochastic process with respect to set-valued Square Integrable Martingale. Then we shall give the Aumann integral measurable theorem, and give the set-valued stochastic Lebesgue integral and set-valued Square Integrable Martingale integral equation. The existence and uniqueness of solution to set-valued stochastic integral equation are proved. The discussion will be useful in optimal control and mathematical finance in psychological factors.
Annika Lang - One of the best experts on this subject based on the ideXlab platform.
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milstein approximation for advection diffusion equations driven by multiplicative noncontinuous Martingale noises
Applied Mathematics and Optimization, 2012Co-Authors: Andrea Barth, Annika LangAbstract:In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, cadlag, Square Integrable Martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L2 and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler-Maruyama approximation. Finally, simulations complete the paper.© Springer Science+Business Media, LLC 2012.
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almost sure convergence of a galerkin approximation for spdes of zakai type driven by Square Integrable Martingales
Journal of Computational and Applied Mathematics, 2012Co-Authors: Annika LangAbstract:This work describes a Galerkin type method for stochastic partial differential equations of Zakai type driven by an infinite dimensional cadlag Square Integrable Martingale. Error estimates in the semidiscrete case, where discretization is only done in space, are derived in L^p and almost sure senses. Simulations confirm the theoretical results.
L I Shikai - One of the best experts on this subject based on the ideXlab platform.
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Square Integrable Martingale
Fuzzy systems and mathematics, 2008Co-Authors: L I ShikaiAbstract:In this paper,set-valued squire integral Martingale and real-valued squire integral Martingale are given.It will take an important role in the deeper research of set-valued stochastic analysis.