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On large deviations in testing Ornstein–Uhlenbeck-type models

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Abstract

We obtain exact large deviation rates for the log-likelihood ratio in testing models with observed Ornstein–Uhlenbeck processes and get explicit rates of decrease for the error probabilities of Neyman–Pearson, Bayes, and minimax tests. Moreover, we give expressions for the rates of decrease for the error probabilities of Neyman–Pearson tests in models with observed processes solving affine stochastic delay differential equations.

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Authors and Affiliations

  1. Weierstraß Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, Berlin, 10117, Germany

    Pavel V. Gapeev

  2. Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya Str. 65, Moscow, 117997, Russia

    Pavel V. Gapeev

  3. Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Uwe Küchler

Authors
  1. Pavel V. Gapeev
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  2. Uwe Küchler
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Correspondence to Pavel V. Gapeev.

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Gapeev, P.V., Küchler, U. On large deviations in testing Ornstein–Uhlenbeck-type models. Stat Infer Stoch Process 11, 143–155 (2008). https://doi.org/10.1007/s11203-007-9012-1

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  • DOI: https://doi.org/10.1007/s11203-007-9012-1

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