The Robbins-Monro type stochastic differential equations. III. Polyak's averaging

Abstract

General results concerning the asymptotic behaviour of the Polyak averaging of the solution of the Robbins-Monro type stochastic differential equation are presented. It is shown that the suitable normalized process admits an asymptotic expansion which enables one to obtain its asymptotic distribution from a central limit theorem for martingales.

Keywords:

• stochastic approximation
• Robbins-Monro type SDE
• recursive estimation
• Polyak's averaging

AMS Subject Classification::

• 62L20
• 60H10

Acknowledgement

We express our thanks to anonymous referees for careful reading and useful suggestions.