On Averaged Control and Iteration Improvement for a Class of Multidimensional Ergodic Diffusions

The paper is devoted to the derivation of ergodic Bellman’s equation for a special case of a uniformly ergodic multidimensional controlled diffusion with variable diffusion and drift coefficients both depending on control; the diffusion coefficient must be a scalar function. The convergence of Howard’s iterative reward improvement algorithm to the unique solution of Bellman’s equation is also established.