Summary: Convergence of stochastic approximation for Lyapunov stable
dynamics: a proof from ...rst principles.
- Éric Moulines2
- Stanislav Volkov1
School of Mathematics, University of Bristol
July 13, 2004
In this short note we present a proof, aimed at beginners, of the convergence of the stochastic
approximation recursion i+1 = i + i+1h( i)+ i+1 i+1 under the classical 0-level Kushner-Clark noise
condition when the underlying dynamic is Lyapunov stable. The technique of proof relies on simple
calculus arguments and bypasses the need for the introduction of the associated continuous time ODE.
Future work includes the extension of the result to the case where the 0-level Kushner-Clark condition
is replaced with a r-level condition for r > 0 .
We study the convergence of the recursion
i+1 = i + i+1h( i) + i+1 i+1;
for a given function h : ! Rn