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On Large Deviations in Testing Ornstein-Uhlenbeck Type Models with Delay

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  • Küchler, Uwe
  • Gapeev, Pavel V.

Abstract

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

Suggested Citation

  • Küchler, Uwe & Gapeev, Pavel V., 2003. "On Large Deviations in Testing Ornstein-Uhlenbeck Type Models with Delay," SFB 373 Discussion Papers 2003,45, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200345
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    1. Gushchin, Alexander A. & Küchler, Uwe, 2001. "On parametric statistical models for stationary solutions of affine stochastic delay differential equations," SFB 373 Discussion Papers 2001,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Gushchin, Alexander A. & Küchler, Uwe, 2000. "On stationary solutions of delay differential equations driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 195-211, August.
    3. Gushchin, Alexander A. & Kuchler, Uwe, 1997. "Asymptotic inference for a linear stochastic differential equation with time delay," SFB 373 Discussion Papers 1997,43, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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