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Journal of Applied Mathematics and Stochastic Analysis
Volume 2004, Issue 2, Pages 137-141
http://dx.doi.org/10.1155/S1048953304308026

A description of stochastic systems using chaotic maps

Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Québec H4B 1R6, Canada

Received 28 August 2003; Revised 4 February 2004

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let ρ(x,t) denote a family of probability density functions parameterized by time t. We show the existence of a family {τ1:t>0} of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are precisely ρ(x,t). In particular, we are interested in the densities that arise from the diffusions. We derive a partial differential equation whose solution yields the family of chaotic maps whose density functions are precisely those of the diffusion.