Stochastic approximation with long range dependent and heavy tailed noise

Authors:
V. Anantharam;V. S. Borkar
Affiliations:
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA 94720;Department of Electrical Engineering, Indian Institute of Technology, Powai, India 400076
Venue:
Queueing Systems: Theory and Applications
Year:
2012

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Abstract

Stability and convergence properties of stochastic approximation algorithms are analyzed 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. The proofs are based on comparing suitably interpolated iterates with a limiting ordinary differential equation. Related issues such as asynchronous implementations, Markov noise, etc. are briefly discussed.