Stochastic homogenization of viscous superquadratic Hamilton-Jacobi   equations in dynamic random environment
  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. 
Wenjia Jing, Panagiotis E. Souganidis, Hung V. Tran
math.AP math.OC math.PR