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Learning models with continuous time parameter and multivariate point processes

Published online by Cambridge University Press:  14 July 2016

Helmut Pruscha
Helmut Pruscha*
Affiliation:
University of Munich
*
∗ Postal address: University of Munich, Mathematical Institute, Theresienstr. 39, D-8000 München 2, West Germany.
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Abstract

The concept of a learning model (or random system with complete connections) with continuous time parameter is introduced on the basis of the notion of a multivariate point process possessing an intensity. The stepwise transition probabilities in terms of the intensity are derived and a Monte Carlo method for simulating a sample is presented. By modelling the intensity process various types of learning models can be built. We propose a linear learning model which comprises the continuous-time Markov process as well as Hawkes's mutually exciting point process. We study the asymptotic behaviour of this linear model in terms of explosion or extinction and of convergence of some estimates. We close with some numerical results from computer simulations.

Keywords

RANDOM SYSTEM WITH COMPLETE CONNECTIONSINTENSITY PROCESSSIMULATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 884 - 890
Copyright
Copyright © Applied Probability Trust 1983 

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