Mathematical Problems in Engineering
Volume 5 (1999), Issue 1, Pages 33-54

A model discrimination method for processes with different memory structure

Mark Freidlin and Ruth Pfeiffer

Department of Mathematics, University of Maryland, College Park, 20742, MD, USA

Received 14 July 1998; Revised 5 November 1998

Copyright © 1999 Mark Freidlin and Ruth Pfeiffer. 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.


In this paper we develop a test for determining whether the observed sample path comes from a system with hysteresis perturbed by noise, or if it arises from a system governed by an ordinary differential equation with the same noise. A large sample size test is constructed, which is appropriate in many practical situations. Two models are considered as alternatives to the hysteresis model. An asymptotic expression for the cutoff point of the test is found using a version of the central limit theorem.