ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 62M Pfeiffer, Ruth, University of Maryland, USA Statistical Problems for Stochastic Processes with Hysteresis We consider a system with hysteresis: the motion of a particle is governed by one of two stochastic differential equations depending on which of two thresholds x_{0} and x_{1}, x_{1} > x_{0} was crossed last. The first problem considered is an estimation problem: Using observations of the process over a fixed time interval we construct the maximum likelihood estimator for the unknown threshold x_{1}. A close connection to the order statistics allows to calculate the asymptotic characteristics of the estimator. We also present a test to determine 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. Reference: M. I. Freidlin, R. Pfeiffer, A Threshold Estimation Problem for Stochastic Processes with Hysteresis, Statistics and Probability Letters vol 36, n4, (1998), pp337.