ON ITERATION IMPROVEMENT FOR AVERAGED EXPECTED COST CONTROL FOR ONE-DIMENSIONAL ERGODIC DIFFUSIONS

摘要

An ergodic Bellman's (Hamilton-Jacobi-Bellman) equation is proved for a uniformly ergodic one-dimensional controlled diffusion with variable diffusion and drift coefficients both depending on control; convergence of the values provided by Howard's reward improvement algorithm to the value which is a component of the unique solution of Bellman's equation is established.