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

Arthur Yosef ()
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Arthur Yosef: Tel Aviv-Yaffo Academic College

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1366-1381

Abstract: 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.

Keywords: Fractional Brownian motion; Set-indexed; Stationary increment; Self-similarity; Continuity; Differentiability; 60J65; 60G15; 60G17 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-021-01077-6

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