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Large and Moderate Deviations for Estimators of Quadratic Variational Processes of Diffusions

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Abstract

For a diffusion process dXt = σdB t + b(t, Xt)dt with (σ t ) unknown, we study the large and moderate deviations of the estimator \(\bar \Theta _n (t): = \sum\nolimits_{k = 0}^{\left[ {nt} \right]} {(X_{k/n} - X_{(k - 1)/n} )^2 } \) of the quadratic variational process \(\Theta (t) = \int_0^t {\sigma _s^2 {\text{d}}} s\).

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, CNRS-UMR 6620 Université Blaise Pascal, 63177, Aubiere, France

    Hacène Djellout, Arnaud Guillin & Liming Wu

Authors
  1. Hacène Djellout
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  2. Arnaud Guillin
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  3. Liming Wu
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Djellout, H., Guillin, A. & Wu, L. Large and Moderate Deviations for Estimators of Quadratic Variational Processes of Diffusions. Statistical Inference for Stochastic Processes 2, 195–225 (1999). https://doi.org/10.1023/A:1009950229386

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  • DOI: https://doi.org/10.1023/A:1009950229386

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