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Computing limiting stationary distributions of small noisy networks

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Fred Richman  and
Katarzyna Winkowska-Nowak
Fred Richman*
Affiliation:
Florida Atlantic University
Katarzyna Winkowska-Nowak*
Affiliation:
University of Warsaw
*
∗ Postal address: Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431, USA. Email address: [email protected]
∗∗ Postal address: Institute for Social Studies, University of Warsaw, Stawki 5/7, 00-183 Warsaw, Poland.
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Abstract

The dynamics of opinion transformation is modeled by a neural network with a nonnegative matrix of connections. Noise is introduced at each site, and the limit of the stationary distributions of the resulting Markov chains as the noise goes to zero is taken as an indication of what configurations will be seen. An algorithm for computing this limit is given, and a number of examples are worked out. Some of the mathematical ideas developed, such as visible states, time scales, and a calculus of indexed probabilities, are of independent interest.

Keywords

Markovnoisynetwork

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 60J22: Computational methods in Markov chains
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 161 - 178
Copyright
Copyright © Applied Probability Trust 2002 

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