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Distances and discrimination rates for stochastic processes. (English) Zbl 0701.62084

Summary: We consider Rényi distances which are representing Hellinger integrals and Kullback-Leibler divergences. Basic functional properties are established for these and other convex distances. We evaluate Rényi distances for distributions of regular Markov processes. They are shown to be proportional to Fisher informations of corresponding Markov kernels. Rate of discrimination between two regular Markov processes is investigated using the Rényi distances. In particular, asymptotic formulas are established for the second kind error of Neyman-Pearson tests, and for the mixed error of Bayes tests.

MSC:

62M02 Markov processes: hypothesis testing
62F05 Asymptotic properties of parametric tests
62F15 Bayesian inference
62B10 Statistical aspects of information-theoretic topics
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