Rezakhanlou, Fraydoun Central limit theorem for stochastic Hamilton-Jacobi equations. (English) Zbl 0972.60054 Commun. Math. Phys. 211, No. 2, 413-438 (2000). 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. Reviewer: H.Pragarauskas (Vilnius) Cited in 6 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60F05 Central limit and other weak theorems 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games Keywords:asymptotic behaviour; Hamilton-Jacobi equation PDFBibTeX XMLCite \textit{F. Rezakhanlou}, Commun. Math. Phys. 211, No. 2, 413--438 (2000; Zbl 0972.60054) Full Text: DOI