Article ID Journal Published Year Pages File Type
4665025 Advances in Mathematics 2017 20 Pages PDF
Abstract

We prove that the solution of the discounted approximation of a degenerate viscous Hamilton–Jacobi equation with convex Hamiltonians converges to that of the associated ergodic problem. We characterize the limit in terms of stochastic Mather measures by using the nonlinear adjoint method and deriving a commutation lemma. This convergence result was first proven by Davini, Fathi, Iturriaga, and Zavidovique for first order Hamilton–Jacobi equations.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
Authors
, ,