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Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment (1606.06409v2)
Published 21 Jun 2016 in math.AP, math.OC, and math.PR
Abstract: We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient) we establish a homogenization result and characterize the effective Hamiltonian for arbitrary (possibly degenerate) elliptic diffusion matrices. The result extends previous work that required uniform ellipticity and space-time homogeneity for the diffusion.