The sample-based value function in discounted infinite-horizon stochastic control converges to a Gaussian process limit that solves a linear DP-type fixed-point equation.
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Asymptotic Analysis of Empirical Dynamic Programming in Infinite-Horizon Stochastic Optimal Control
The sample-based value function in discounted infinite-horizon stochastic control converges to a Gaussian process limit that solves a linear DP-type fixed-point equation.