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arXiv · 1303.0618

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

Ari Arapostathis·Vivek S. Borkar·K. Suresh Kumar
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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.

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Ari Arapostathis, Vivek S. Borkar, K. Suresh Kumar. 2013-03-04. Convergence of The Relative Value Iteration for the Ergodic Control Problem of Nondegenerate Diffusions under Near-Monotone Costs. https://doi.org/10.1137/130912918

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