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

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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.

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  1. Tel Aviv-Yaffo Academic College, 2 Rabenu Yeruham st, Tel Aviv-Yaffo, Israel

    Arthur Yosef

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  1. Arthur Yosef
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Yosef, A. Selected Topics in the Generalized Mixed Set-Indexed Fractional Brownian Motion. J Theor Probab 34, 1366–1381 (2021). https://doi.org/10.1007/s10959-021-01077-6

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  • DOI: https://doi.org/10.1007/s10959-021-01077-6

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