Exact and approximate correctors for stochastic Hamiltonians: The 1-dimensional case (Q734958)

Given a \(1-\) dimensional ergodic dynamical system \((\tau_x)_{x\in \mathbb{R}}\) on a probability space \((\Omega, F,P)\), it is considered a stationary Hamiltonian \(H(x,p,\omega),\) defined in \(\mathbb{R}\times \mathbb{R}\times\Omega,\) enjoying suitable continuity, quasiconvexity and coercivity conditions, and the family of stochastic Hamilton-Jacobi equations \[ H(x, v^{\prime}(x,\omega),\omega)=a. \] The authors perform a qualitative investigation of critical Hamilton-Jacobi equations: show the existence of approximate correctors, give characterizing conditions for the existence of correctors, provide Lax-type representation formulae and establish comparison principles.