On the $p$th variation of a class of fractal functions

DOI10.1090/PROC/15171zbMath1471.60079arXiv1909.05239OpenAlexW3026403835MaRDI QIDQ5130885

Alexander Schied, Zhenyuan Zhang

Publication date: 29 October 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.05239

zbMATH Keywords

Takagi-van der Waerden functionsWeierstraß function\(p\)th variationpathwise Itô calculus(non-symmetric) infinite Bernoulli convolution and its moments

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Stochastic integrals (60H05) Fractals (28A80) Functions of bounded variation, generalizations (26A45)

Related Items (4)

A probabilistic approach to the \(\varPhi \)-variation of classical fractal functions with critical roughness ⋮ Bilinear equations in Hilbert space driven by paths of low regularity ⋮ mu-Brownian motion, dualities, diffusions, transforms, and reproducing kernel Hilbert spaces ⋮ A limit theorem for Bernoulli convolutions and the \(\Phi \)-variation of functions in the Takagi class

Cites Work

• Unnamed Item
• Unnamed Item
• Probabilistic aspects of finance
• The Takagi function: a survey
• Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index \(H\geq\frac 1 4\).
• On (signed) Takagi-Landsberg functions: \(p\)th variation, maximum, and modulus of continuity
• Moments of infinite convolutions of symmetric Bernoulli distributions
• Stochastic calculus for fractional Brownian motion and related processes.
• \(n\)-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes.
• Dimension of the Graphs of the Weierstrass-Type Functions
• On the Hausdorff dimension of some fractal sets
• Fractal Dimensions and Singularities of the Weierstrass Type Functions
• Model-Free Portfolio Theory and Its Functional Master Formula
• Volatility is rough
• Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity
• Examples of Itô càdlàg rough paths
• A course on rough paths. With an introduction to regularity structures

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