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Properties and distribution of the dynamical functional for the fractional Gaussian noise

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  • Loch-Olszewska, Hanna

Abstract

The fractional Brownian motion and its increment process, the fractional Gaussian noise (fGn), are highly popular models for data exhibiting anomalous diffusion. In this paper, an explicit formula for the dynamical functional, a tool for testing ε-ergodicity breaking and a statistic helpful in the process identification, is provided for the fractional Gaussian noise. Its basic characteristics are derived and the distribution of its single trajectory estimator is studied. Additionally, the sensibility of the convergence of the dynamical functional to the Hurst parameter H is analysed.

Suggested Citation

  • Loch-Olszewska, Hanna, 2019. "Properties and distribution of the dynamical functional for the fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 252-271.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:252-271
    DOI: 10.1016/j.amc.2019.03.038
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    References listed on IDEAS

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    1. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    2. Titiwat Sungkaworn & Marie-Lise Jobin & Krzysztof Burnecki & Aleksander Weron & Martin J. Lohse & Davide Calebiro, 2017. "Single-molecule imaging reveals receptor–G protein interactions at cell surface hot spots," Nature, Nature, vol. 550(7677), pages 543-547, October.
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    Cited by:

    1. Janczura, Joanna & Burnecki, Krzysztof & Muszkieta, Monika & Stanislavsky, Aleksander & Weron, Aleksander, 2022. "Classification of random trajectories based on the fractional Lévy stable motion," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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