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Properties and Hurst exponent estimation of the circularly-symmetric fractional Brownian motion

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  • Coeurjolly, Jean-François
  • Porcu, Emilio

Abstract

This paper extends the fractional Brownian motion to the complex-valued case. The model is defined as the centered, zero at zero, self-similar complex-valued stochastic process with stationary increments. We present a few properties of this new model and propose an estimation of its main index, the Hurst exponent characterizing the self-similarity property.

Suggested Citation

  • Coeurjolly, Jean-François & Porcu, Emilio, 2017. "Properties and Hurst exponent estimation of the circularly-symmetric fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 21-27.
    • Handle: RePEc:eee:stapro:v:128:y:2017:i:c:p:21-27
    DOI: 10.1016/j.spl.2017.04.005
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    References listed on IDEAS

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    1. 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.
    2. 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.
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