Ergodic Type Bellman Equations of Risk-Sensitive Control

Abstract

Ergodic type Bellman equations of risk-sensitive control in general cases are considered. We study the existence of solutions of the equations relating to the eigenvalue problem of Schödinger operators. Furthermore, by taking their singular limits, we obtain particular viscosity solutions of Hamilton-Jacobi-Isaacs equations of differential games which correspond to nolinear H_∞-control problems.