On 1D ergodic controlled diffusion

This is a joint work in progress with S. Anulova (IPU) and H. Mai (CREST, Paris). For a uniformly stable controlled diffusion with an average cost function we establish "ergodic Bellman's equation" and prove uniqueness of its solution. A "Reward Improvement Algorithm" also known under several other names is studied: it provides a successive approximation to the solution. Recently ergodic control became a topical area. In comparison to the earlier results, we add control in the diffusion coefficient.