Sample path properties of the fractional Wiener–Weierstrass bridge
Abstract
Fractional Wiener--Weierstrass bridges are a class of Gaussian processes that arise from replacing the trigonometric function in the construction of classical Weierstrass functions by a fractional Brownian bridge. We investigate the sample path properties of such processes, including local and uniform moduli of continuity, $Φ$-variation, Hausdorff dimension, and location of the maximum. Our analysis relies heavily on upper and lower bounds of fractional integrals, where we establish a novel improvement of the classical Hardy--Littlewood inequality for fractional integrals of a special class of step functions.
Fields of Study & Subjects
Acoustic Wave Phenomena Research
Digital Filter Design and Implementation
Electromagnetic Compatibility and Noise Suppression
Publication details
- Journal / source
- Bernoulli
- Volume
- 32
- Issue
- 3
- Publication date
- 29 April 2026
- Language
- EN