A Sublinear Variance Bound for Solutions of a Random Hamilton-Jacobi Equation

Journal Article

We estimate the variance of the value function for a random optimal control problem. The value function is the solution w ε of a Hamilton-Jacobi equation with random Hamiltonian H(p, x, ω)=K(p)-V(x/ε, ω) in dimension d ≥ 2. It is known that homogenization occurs as ε → 0, but little is known about the statistical fluctuations of w ε. Our main result shows that the variance of the solution w ε is bounded by O(ε/{pipe}log ε {pipe}). The proof relies on a modified Poincaré inequality of Talagrand. © 2012 Springer Science+Business Media, LLC.

Full Text

Duke Authors

Cited Authors

  • Matic, I; Nolen, J

Published Date

  • 2012

Published In

Volume / Issue

  • 149 / 2

Start / End Page

  • 342 - 361

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/s10955-012-0590-y