The Robbins–Monro type stochastic differential equations. II. Asymptotic behaviour of solutions

Abstract

General results concerning the asymptotic behaviour of the solution of the Robbins–Monro type stochastic differential equations are presented. In particular, the rate of convergence of the solution Z = (Z_{t})_{t \qeq 0} as t \rightarrow \infty is established. Moreover, it is shown that Z admits an asymptotic expansion which enables one to obtain the asymptotic distribution of the randomly normed solution from a martingale limit theorem.

Keywords:

• Stochastic approximation
• Robbins–Monro type SDE
• recursive estimation
• 62L20
• 60H10

Notes

^†Supported by Grant INTAS 97-30204.