A threshold estimation problem for processes with hysteresis

Mark Freidlin and Ruth Pfeiffer

Statistics & Probability Letters, 1998, vol. 36, issue 4, 337-347

Abstract: 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 0 and x1,x1 > 0 was crossed last. Using observations of the process over a fixed time interval we construct the maximum likelihood estimator for the unknown threshold x1. A close connection to the order statistics allows to calculate the asymptotic characteristics of the estimator.

Keywords: Hysteresis; Stochastic; processes; Threshold; estimation; Maximum; likelihood; method; Asymptotic; properties; Nonregular; asymptotics (search for similar items in EconPapers)
Date: 1998
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