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Averaging analysis of a point process adaptive algorithm

Part of: Qualitative theory Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

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

Keywords

Averagingpoint processadaptive algorithm

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 34C29: Averaging method 60G55: Point processes
Type
Part 6. Stochastic processes
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 361 - 372
Copyright
Copyright © Applied Probability Trust 2004 

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