Convergence of The Relative Value Iteration for the Ergodic Control Problem of Nondegenerate Diffusions under Near-Monotone Costs

Abstract

We study the relative value iteration for the ergodic control problem under a near-monotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasilinear parabolic Cauchy initial value problem in $\RR^{d}$. We show that this Cauchy problem stabilizes, or in other words, that the solution of the quasilinear parabolic equation converges for every bounded initial condition in $\Cc^{2}(\RR^{d})$ to the solution of the Hamilton--Jacobi--Bellman (HJB) equation associated with the ergodic control problem.

References in corpus (3)

• Downside risk minimization via a large deviations approach
• A Relative Value Iteration Algorithm for Non-degenerate Controlled Diffusions
• Relative Value Iteration for Stochastic Differential Games

Cited by in corpus (4)

• On Solutions of Mean Field Games with Ergodic Cost
• On uniform exponential ergodicity of Markovian multiclass many-server queues in the Halfin-Whitt regime
• Average cost optimal control under weak ergodicity hypotheses: Relative value iterations
• Optimal Ergodic Control of Linear Stochastic Differential Equations with Quadratic Cost Functionals Having Indefinite Weights