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On large deviations of empirical measures for stationary Gaussian processes

Author

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  • Bryc, Wlodzimierz
  • Dembo, Amir

Abstract

We show that the large deviation principle with respect to the weak topology holds for the empirical measure of any stationary continuous-time Gaussian process with continuous vanishing at infinity spectral density. We also point out that large deviation principle might fail in both continuous and discrete time if the spectral density is discontinuous.

Suggested Citation

  • Bryc, Wlodzimierz & Dembo, Amir, 1995. "On large deviations of empirical measures for stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 23-34, July.
    • Handle: RePEc:eee:spapps:v:58:y:1995:i:1:p:23-34
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    Cited by:

    1. Włodzimierz Bryc & Amir Dembo, 1997. "Large Deviations for Quadratic Functionals of Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 10(2), pages 307-332, April.
    2. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.
    3. Heck, Matthias K., 1998. "The principle of large deviations for the almost everywhere central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 61-75, August.

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