A viscous ergodic problem with unbounded and measurable ingredients. Part 1: HJB Equation

Abstract

We address the problem of existence and uniqueness of solutions $(c,u(\cdot ))$ to ergodic Hamilton-Jacobi-Bellman (HJB) equations of the form $H(x,\nabla u(x),D^{2}u(x))=c$ in the whole space ${\mathbb{R}}^m$ with unbounded and merely measurable data and where $H$ is a Bellman Hamiltonian. The method we use is different from classical approaches. It relies on duality theory and optimization in abstract Banach spaces together with maximal dissipativity of the diffusion operator.

arXiv commentTo be published in SIAM Journal on Control and Optimization (SICON)