Decision and estimation statistical theory share with information theory the common outlook of optimally using a set of random data, so this fields have been coming close together. Solved problems are particular cases in the generalizations of classical hypotheses testing and in relatively recent studies of statistical identification of distributions of randomly acting objects. The main aim of the present investigation is to solve the problem of studying the matrix E of error probabilities exponents of the optimal test for L > 2 hypotheses by using the theory of large deviations for one and two independent objects. The second aim is solution of the problem of identification under reliability requirements of hypotheses concerning distribution of Markov simple homogenous stationary chain with a finite number of states. The study of this book recommend for Master and PhD students and Scientific research in branches of Applied mathematics, Statistics and also in Engineering.