  We consider a recursive iterative algorithm for identification of parameters
of the Preisach model, one of the most commonly used models of hysteretic
input-output relationships. The classical identification algorithm due to
Mayergoyz defines explicitly a series of test inputs that allow one to find
parameters of the Preisach model with any desired precision provided that (a)
such input time series can be implemented and applied; and, (b) the
corresponding output data can be accurately measured and recorded. Recursive
iterative identification schemes suitable for a number of engineering
applications have been recently proposed as an alternative to the classical
algorithm. These recursive schemes do not use any input design but rather rely
on an input-output data stream resulting from random fluctuations of the input
variable. Furthermore, only recent values of the input-output data streams are
available for the scheme at any time instant. In this work, we prove
exponential convergence of such algorithms, estimate explicitly the convergence
rate, and explore which properties of the stochastic input and the algorithm
affect the guaranteed convergence rate.
