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Selected Topics in the Generalized Mixed Set-Indexed Fractional Brownian Motion

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  • Arthur Yosef

    (Tel Aviv-Yaffo Academic College)

Abstract

In this paper, we explore the generalized mixed fractional Brownian motion in the set-indexed framework and generalize several recent results from Miao et al. (Lecture Notes and Math, Springer, New York, 2008), Zili (J. Appl. Math. Stoch. Anal. 30:1–9, 2006) and Thale (Appl. Math. Sci. 3(28):1885–1901, 2009). We present the characterization of generalized mixed set-indexed fractional Brownian motion (gmsifBM) by flows, and we extend some selected aspects to the gmsifBM for the following issues: stationary increments, self-similarity, long-range dependence, Hölder continuity, differentiability, Hausdorff dimension, etc.

Suggested Citation

  • Arthur Yosef, 2021. "Selected Topics in the Generalized Mixed Set-Indexed Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1366-1381, September.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-021-01077-6
    DOI: 10.1007/s10959-021-01077-6
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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. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
    3. Mounir Zili, 2006. "On the mixed fractional Brownian motion," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-9, August.
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