The Experts below are selected from a list of 71655 Experts worldwide ranked by ideXlab platform
Marek Biskup - One of the best experts on this subject based on the ideXlab platform.
-
a central Limit Theorem for the effective conductance linear boundary data and small ellipticity contrasts
Communications in Mathematical Physics, 2014Co-Authors: Marek Biskup, Michele Salvi, Tilman WolffAbstract:Given a resistor network on \({\mathbb{Z}^d}\) with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic Limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central Limit Theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
-
a central Limit Theorem for the effective conductance linear boundary data and small ellipticity contrasts
arXiv: Probability, 2012Co-Authors: Marek Biskup, Michele Salvi, Tilman WolffAbstract:Given a resistor network on $\mathbb Z^d$ with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic Limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central Limit Theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
Mohamed Ben Alaya - One of the best experts on this subject based on the ideXlab platform.
-
Central Limit Theorem for the multilevel Monte Carlo Euler method
Annals of Applied Probability, 2015Co-Authors: Mohamed Ben Alaya, Ahmed Kebaier, Mohamed Ben AlayaAbstract:This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central Limit Theorem of Lindeberg-Feller type for the multilevel Monte Carlo method associated with the Euler discretization scheme. To do so, we prove first a stable law convergence Theorem, in the spirit of Jacod and Protter [Ann. Probab. 26 (1998) 267-307], for the Euler scheme error on two consecutive levels of the algorithm. This leads to an accurate description of the optimal choice of parameters and to an explicit characterization of the Limiting variance in the central Limit Theorem of the algorithm. A complexity of the multilevel Monte Carlo algorithm is carried out.
Tilman Wolff - One of the best experts on this subject based on the ideXlab platform.
-
a central Limit Theorem for the effective conductance linear boundary data and small ellipticity contrasts
Communications in Mathematical Physics, 2014Co-Authors: Marek Biskup, Michele Salvi, Tilman WolffAbstract:Given a resistor network on \({\mathbb{Z}^d}\) with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic Limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central Limit Theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
-
a central Limit Theorem for the effective conductance linear boundary data and small ellipticity contrasts
arXiv: Probability, 2012Co-Authors: Marek Biskup, Michele Salvi, Tilman WolffAbstract:Given a resistor network on $\mathbb Z^d$ with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic Limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central Limit Theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
Lingjiong Zhu - One of the best experts on this subject based on the ideXlab platform.
-
central Limit Theorem for nonlinear hawkes processes
Journal of Applied Probability, 2013Co-Authors: Lingjiong ZhuAbstract:The Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central Limit Theorem for the nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.
-
central Limit Theorem for nonlinear hawkes processes
arXiv: Probability, 2012Co-Authors: Lingjiong ZhuAbstract:Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. In this paper, we obtain a functional central Limit Theorem for nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.
Mohamed Ben Alaya - One of the best experts on this subject based on the ideXlab platform.
-
Central Limit Theorem for the multilevel Monte Carlo Euler method
Annals of Applied Probability, 2015Co-Authors: Mohamed Ben Alaya, Ahmed Kebaier, Mohamed Ben AlayaAbstract:This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central Limit Theorem of Lindeberg-Feller type for the multilevel Monte Carlo method associated with the Euler discretization scheme. To do so, we prove first a stable law convergence Theorem, in the spirit of Jacod and Protter [Ann. Probab. 26 (1998) 267-307], for the Euler scheme error on two consecutive levels of the algorithm. This leads to an accurate description of the optimal choice of parameters and to an explicit characterization of the Limiting variance in the central Limit Theorem of the algorithm. A complexity of the multilevel Monte Carlo algorithm is carried out.
