Classical Adjoints for Ergodic Stochastic Control

Abstract

In this paper we consider ergodic optimal control of a diffusion process $\{X_t^u{\}}_{t\ge 0}$, taking values in $\bR^n$, where both drift and volatility are controlled. We establish a novel strong duality between the existence of a unique solution to the infinite horizon adjoint BSDE and strong dissipativity of $X^u$. We then proceed to show that the latter implies irreducibility, the strong Feller property and exponential ergodicity. We conclude by discussing the connection with ergodic BSDEs.

References in corpus (1)

• Ergodic BSDEs with jumps and time dependence

Cited by in corpus (1)

• Ergodic BSDE with an unbounded and multiplicative underlying diffusion and application to large time behavior of viscosity solution of HJB equation