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Mathematical Problems of Computer Science 31, 49{59, 2008.

On Optimal H ypothesis T esting for P air of

Stochastically Coupled Objects.

E vg u e n i A . H a r o u t u n ia n a n d A r a m O. Y e s s a ya n

Institute for Informatics and Automation Problems of NAS of RA

e-mail: eghishe@sci.am

Abstract

The paper is devoted to hypotheses testing for a model consisting of two stochas-
tically coupled objects. It is supposed that L1 possible probability distributions are
known for the ¯rst object and the second object is distributed according to one of
L1 £ L2 given conditional distributions depending on the distribution index and the
current observed state of the ¯rst object. The matrix of interdependencies of all pos-
sible pairs of the error probability exponents in asymptotically optimal tests of dis-
tributions of both objects is studied. The case of two objects which cannot have the
same probability distribution from two possible variants was considered by Ahlswede
and Haroutunian. This case for three hypotheses and the model of two statistically
dependent objects for two hypotheses were examined by Haroutunian and Yessayan.

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