Asymptotic normality of randomly truncated stochastic algorithms

Jérôme Lelong (1)

1 MATHFI - Mathématiques financières

We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly easy to check in practice.

Mots clés: stochastic approximation; martingale arrays; central limit theorem; randomly truncated stochastic algorithms

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Jérôme Lelong. Asymptotic normality of randomly truncated stochastic algorithms. ESAIM: Probability and Statistics, 2013, 17, pp.105-119. ⟨10.1051/ps/2011110⟩. ⟨hal-00464380v2⟩