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Uniform Hölder exponent of a stationary increments Gaussian process: Estimation starting from average values

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  • Peng, Qidi

Abstract

Let be a stationary increments Gaussian process satisfying some assumptions. By using the notion of generalized quadratic variation we build a strongly consistent and asymptotically normal estimator of the uniform Hölder exponent of X, over a compact interval. Our estimator is obtained starting from average values of the process over a regular grid.

Suggested Citation

  • Peng, Qidi, 2011. "Uniform Hölder exponent of a stationary increments Gaussian process: Estimation starting from average values," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1326-1335, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1326-1335
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    References listed on IDEAS

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    1. Benassi, Albert & Cohen, Serge & Istas, Jacques & Jaffard, Stéphane, 1998. "Identification of filtered white noises," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 31-49, June.
    2. Ayache, Antoine & Lévy Véhel, Jacques, 2004. "On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 119-156, May.
    3. Gloter, A. & Hoffmann, M., 2004. "Stochastic volatility and fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 113(1), pages 143-172, September.
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