Path Properties of a Generalized Fractional Brownian Motion

Tomoyuki Ichiba; Guodong Pang; Murad S. Taqqu

doi:10.1007/s10959-020-01066-1

Path Properties of a Generalized Fractional Brownian Motion

Tomoyuki Ichiba, Guodong Pang, Murad S. Taqqu

Marcus Department of Industrial and Manufacturing Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Journal	Journal of Theoretical Probability
DOIs	https://doi.org/10.1007/s10959-020-01066-1
State	Accepted/In press - 2021

All Science Journal Classification (ASJC) codes

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

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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. ",

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doi = "10.1007/s10959-020-01066-1",

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journal = "Journal of Theoretical Probability",

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AU - Ichiba, Tomoyuki

AU - Pang, Guodong

AU - Taqqu, Murad S.

N1 - 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.

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AB - 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.

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