A Gladyshev theorem for trifractional Brownian motion and \(n\)-th order fractional Brownian motion

DOI10.1214/21-ECP422zbMath1481.60080arXiv2105.02385OpenAlexW3202261687MaRDI QIDQ2064839

Xiyue Han

Publication date: 6 January 2022

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.02385

zbMATH Keywords

quadratic variationself-similarity index\(n\)-th order fractional Brownian motiontrifractional Brownian motion

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Sample path properties (60G17)

Cites Work

• A complement to Gladyshev's theorem
• A probabilistic approach to the \(\varPhi \)-variation of classical fractal functions with critical roughness
• A decomposition of the bifractional Brownian motion and some applications
• \(p\)-variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments
• On quadratic variation of processes with Gaussian increments
• Necessary and sufficient conditions for limit theorems for quadratic variations of Gaussian sequences
• Oscillation of sample functions in stationary Gaussian processes
• The Schoenberg--Lévy Kernel and Relationships among Fractional Brownian Motion, Bifractional Brownian Motion, and Others
• A Strong Limit Theorem for Gaussian Processes
• A New Limit Theorem for Stochastic Processes with Gaussian Increments
• Transfer principle for $n$th order fractional Brownian motion with applications to prediction and equivalence in law

This page was built for publication: A Gladyshev theorem for trifractional Brownian motion and \(n\)-th order fractional Brownian motion