Ergodic control problem for one-dimensional diffusions with near-monotone cost
This paper deals with the ergodic control of one-dimensional diffusions, governed by controlled stochastic differential equations. From the dynamic programming point of view, the authors derive Bellman's equation of ergodic control. Assuming a near-monotonicity on the cost function and mild conditions on coefficients, they establish the existence and uniqueness of a solution of Bellman's equation and give necessary and sufficient conditions for optimality of a stable Markov control in terms of the equation.
scientific article; zbMATH DE number 3891208