Central limit theorem for stochastic Hamilton-Jacobi equations
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.
scientific article; zbMATH DE number 1514613