Distances and discrimination rates for stochastic processes

Igor Vajda

Stochastic Processes and their Applications, 1990, vol. 35, issue 1, 47-57

Abstract: We consider Rényi distances which are representing Hellinger integrals and Kullback-Liebler 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.

Keywords: Hellinger; integral; Kullback-Liebler; divergence; Renyi; distance; discrimination; of; Markov; processes; testing; of; hypotheses; about; diffusion; processes (search for similar items in EconPapers)
Date: 1990
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