Abstract
In this paper we present an integral operator that arises in the context of linear dynamical systems, which describes the time evolution of the state probability density function. We propose a finite rank approximation to this integral operator and show that this finite rank operator converges in norm to the integral operator. We discuss Markov chains arising from this finite rank approximation, and show that the eigenvalues of the transition matrices of these Markov chains converge to the eigenvalues of the integral operator as the number of divisions in the statediscretization is increased.
Information
Published: 1 January 1999
First available in Project Euclid: 18 November 2014
zbMATH: 1193.93114
Rights: Copyright © 1999, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
