Abstract:
We study the asymptotic behavior of , where u solves the Hamilton–Jacobi equation u t +H(x,u x ) ≡ 0 with H a stationary ergodic process in the x-variable. It was shown in Rezakhanlou–Tarver [RT] that u ɛ converges to a deterministic function provided H(x,p) is convex in p and the convex conjugate of H in the p-variable satisfies certain growth conditions. In this article we establish a central limit theorem for the convergence by showing that for a class of examples, u ɛ(x,t) can be (stochastically) represented as , where Z(x,t) is a suitable random field. In particular we establish a central limit theorem when the dimension is one and , where ω is a random function that enjoys some mild regularity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 15 February 1999 / Accepted: 14 December 1999
Rights and permissions
About this article
Cite this article
Rezakhanlou, F. Central Limit Theorem¶for Stochastic Hamilton–Jacobi Equations. Comm Math Phys 211, 413–438 (2000). https://doi.org/10.1007/s002200050820
Issue Date:
DOI: https://doi.org/10.1007/s002200050820