Stochastic approximation with ‘bad’ noise (extended abstract)

It is well known that the noise processes in the Internet and several other situations arising in communications exhibit long range dependent and heavy tailed behaviour, a fact which has also been theoretically justified through limit theorems such as that of Mikosch, Resnick, Rootzen and Stegeman. Motivated by this, we consider stability and convergence properties of stochastic approximation algorithms when the noise includes a long range dependent component (modeled by a fractional Brownian motion) and a heavy tailed component (modeled by a symmetric stable process), in addition to the usual ´martingale noise´. This is motivated by the emergent applications in communications.