@article{2dc10e9359f34d419b661be1d0cf5641,
title = "Path Properties of a Generalized Fractional Brownian Motion",
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 H{\"o}lder continuity, path differentiability/non-differentiability, and functional and local law of the iterated logarithms.",
author = "Tomoyuki Ichiba and Guodong Pang and Taqqu, {Murad S.}",
note = "Funding Information: The authors are thankful to the reviewers and associate editor for their careful reading and suggestions on various improvements of the paper. In particular, the associate editor pointed out a gap in Sect. in the paper, which led to a significant improvement of our understanding of the process. Tomoyuki Ichiba was supported in part by NSF Grants DMS-1615229 and DMS-2008427. Guodong Pang was supported in part by CMMI-1635410, DMS/CMMI-1715875 and the Army Research Office through Grant W911NF-17-1-0019. Murad S. Taqqu was supported in part by Simons Foundation Grant 569118 at Boston University. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.",
year = "2022",
month = mar,
doi = "10.1007/s10959-020-01066-1",
language = "English (US)",
volume = "35",
pages = "550--574",
journal = "Journal of Theoretical Probability",
issn = "0894-9840",
publisher = "Springer New York",
number = "1",
}