Path Properties of a Generalized Fractional Brownian Motion

Tomoyuki Ichiba (), Guodong Pang () and Murad S. Taqqu ()
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Tomoyuki Ichiba: University of California, Santa Barbara
Guodong Pang: Pennsylvania State University
Murad S. Taqqu: Boston University

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 550-574

Abstract: Abstract The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power-law shape function and non-stationary noises with a power-law variance function. In this paper, we study sample path properties of the generalized fractional Brownian motion, including Hölder continuity, path differentiability/non-differentiability, and functional and local law of the iterated logarithms.

Keywords: Gaussian self-similar process; Non-stationary increments; Generalized fractional Brownian motion; Hölder continuity; Path differentiability/non-differentiability; Functional and local law of the iterated logarithms; 60G05; 60G15; 60G17; 60G18; 60G22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01066-1

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