Path Properties of a Generalized Fractional Brownian Motion

Tomoyuki Ichiba, Guodong Pang, Murad S. Taqqu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)550-574
Number of pages25
JournalJournal of Theoretical Probability
Volume35
Issue number1
DOIs
StatePublished - Mar 2022

All Science Journal Classification (ASJC) codes

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

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