Central limit theorem for stochastic Hamilton-Jacobi equations
type: Item
instance of: scholarly article
title: Central limit theorem for stochastic Hamilton-Jacobi equations
zbMATH Open document ID: 0972.60054
author: Fraydoun Rezakhanlou
published in: Communications in Mathematical Physics
publication date: 2000-10-08T00:00:00Z
review text: The asymptotic behaviour of the solution to the Hamilton-Jacobi equation \(u_t+ H(x,u_x)= 0\) with a random Hamiltonian \(H\) is considered. Sufficient conditions are given, under which \[ \varepsilon u(t/\varepsilon, x/\varepsilon)= \overline u(t,x)+ \sqrt\varepsilon Z(t,x)+ o(\sqrt\varepsilon)\quad\text{as }\varepsilon\to 0, \] where \(\overline u\) is a deterministic function (a solution to the homogenized equation \(\overline u_t+\overline H(\overline u_x)= 0\) with a deterministic Hamiltonian \(\overline H\)) and \(Z(t,x)\) is a random field.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 49L25
zbMATH DE Number: 1514613
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: Hamilton-Jacobi equation
reviewed by: Henrikas Pragarauskas
MaRDI profile type: Publication
full work available at URL: s002200050820
OpenAlex ID: W2603449377
DOI: 10.1007/S002200050820
description: scientific article; zbMATH DE number 1514613