On stochastic ergodic control in infinite dimensions

Abstrakt

Hamilton-Jacobi Bellman equation for the stochastic ergodic control problem is dealt with and the existence and uniqueness of solutions is shown. The formulas for the optimal control and optimal cost are found.

The result is applied to controlled stochastic reaction-diffusion equation.

Klíčová slova

• stochastic
• ergodic
• control
• infinite
• dimensions