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A threshold estimation problem for processes with hysteresis

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  • Freidlin, Mark
  • Pfeiffer, Ruth

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.

Suggested Citation

  • Freidlin, Mark & Pfeiffer, Ruth, 1998. "A threshold estimation problem for processes with hysteresis," Statistics & Probability Letters, Elsevier, vol. 36(4), pages 337-347, January.
    • Handle: RePEc:eee:stapro:v:36:y:1998:i:4:p:337-347
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