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Hurst Index Estimation in Stochastic Differential Equations Driven by Fractional Brownian Motion

Author

Listed:
  • Jan Gairing

    (Ludwig-Maximilians-Universität München)

  • Peter Imkeller

    (Humboldt-Universität zu Berlin)

  • Radomyra Shevchenko

    (Technische Universität Dortmund)

  • Ciprian Tudor

    (CNRS, Université de Lille 1
    Romanian Academy)

Abstract

We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the quadratic variations of the solution, defined via higher-order increments. Then we apply our results to construct and study estimators for the Hurst index.

Suggested Citation

  • Jan Gairing & Peter Imkeller & Radomyra Shevchenko & Ciprian Tudor, 2020. "Hurst Index Estimation in Stochastic Differential Equations Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1691-1714, September.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:3:d:10.1007_s10959-019-00925-w
    DOI: 10.1007/s10959-019-00925-w
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    References listed on IDEAS

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    1. Brouste, Alexandre & Fukasawa, Masaaki & Hino, Hideitsu & Iacus, Stefano & Kamatani, Kengo & Koike, Yuta & Masuda, Hiroki & Nomura, Ryosuke & Ogihara, Teppei & Shimuzu, Yasutaka & Uchida, Masayuki & Y, 2014. "The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i04).
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    3. Jean-François Coeurjolly, 2001. "Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 199-227, May.
    4. Nualart, David & Ouknine, Youssef, 2002. "Regularization of differential equations by fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 103-116, November.
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    Cited by:

    1. Mohamed Hamdouche & Pierre Henry-Labordere & Huy^en Pham, 2023. "Generative modeling for time series via Schr{\"o}dinger bridge," Papers 2304.05093, arXiv.org.
    2. Yongqi Sun & Jianhua Li & Yang Yu & Weijun Zeng, 2022. "Ecological Assessment Based on Remote Sensing Ecological Index: A Case Study of the “Three-Lake” Basin in Yuxi City, Yunnan Province, China," Sustainability, MDPI, vol. 14(18), pages 1-16, September.
    3. Mohamed Hamdouche & Pierre Henry-Labordere & Huyên Pham, 2023. "Generative modeling for time series via Schrödinger bridge," Working Papers hal-04063041, HAL.

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