  This paper deals with the problem of asymptotically optimal detection of
changes in regime-switching stochastic models. We need to divide the whole
obtained sample of data into several sub-samples with observations belonging to
different states of a stochastic models with switching regimes. For this
purpose, the idea of reduction to a corresponding change-point detection
problem is used. Both univariate and multivariate switching models are
considered. For the univariate case, we begin with the study of binary mixtures
of probabilistic distributions. In theorems 1 and 2 we prove that type 1 and
type 2 errors of the proposed method converge to zero exponentially as the
sample size tends to infinity. In theorem 3 we prove that the proposed method
is asymptotically optimal by the rate of this convergence in the sense that the
lower bound in the a priori informational inequality is attained for our
method. Several generalizations to the case of multiple univariate mixtures of
probabilistic distributions are considered. For the multivariate case, we first
study the general problem of classification of the whole array of data into
several sub-arrays of observations from different regimes of a multivariate
stochastic model with switching states. Then we consider regression models with
abnormal observations and switching sets of regression coefficients. Results of
a detailed Monte Carlo study of the proposed method for different stochastic
models with switching regimes are presented.
