Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations

Scott Armstrong (1) , Pierre Cardaliaguet (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of convergence with overwhelming probability under certain structural conditions on the Hamiltonian.

Domaines: Optimisation et contrôle [math.OC]

Scott Armstrong, Pierre Cardaliaguet. Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations. Communications in Partial Differential Equations, 2015, 40 (3), pp.540-600. ⟨10.1080/03605302.2014.971372⟩. ⟨hal-00922714⟩