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Averaging analysis of a point process adaptive algorithm

Published online by Cambridge University Press:  14 July 2016

Victor Solo*
Affiliation:
School of Electrical Engineering, University of New South Wales, Sydney, NSW 2052, Australia. Email address: v.solo@unsw.edu.au

Abstract

Motivated by a problem in neural encoding, we introduce an adaptive (or real-time) parameter estimation algorithm driven by a counting process. Despite the long history of adaptive algorithms, this kind of algorithm is relatively new. We develop a finite-time averaging analysis which is nonstandard partly because of the point process setting and partly because we have sought to avoid requiring mixing conditions. This is significant since mixing conditions often place restrictive history-dependent requirements on algorithm convergence.

Type
Part 6. Stochastic processes
Copyright
Copyright © Applied Probability Trust 2004 

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