Convergence of the Structure Function of a Multifractal Random Walk in a Mixed Asymptotic Setting

DOI10.1080/07362994.2010.503458zbMath1205.60044arXiv0905.3405OpenAlexW2075595941MaRDI QIDQ4932831

Laurent Duvernet

Publication date: 7 October 2010

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.3405

zbMATH Keywords

scaling exponentmultifractal analysismultifractal random walkBrownian motion in multifractal time

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Point estimation (62F10) Singular functions, Cantor functions, functions with other special properties (26A30) Other physical applications of random processes (60K40) Self-similar stochastic processes (60G18)

Related Items

Testing the type of a semi-martingale: Itō against multifractal, On the estimation of the large deviations spectrum, Estimating the scaling function of multifractal measures and multifractal random walks using ratios, Assessing relative volatility/ intermittency/energy dissipation, Multifractal detrended fluctuation analysis: practical applications to financial time series

Cites Work

• Unnamed Item
• \(L^p\)-variations for multifractal fractional random walks
• Spectral representations of infinitely divisible processes
• Sur certaines martingales de Benoit Mandelbrot
• Log-infinitely divisible multifractal processes
• On the Frisch-Parisi conjecture
• Statistical estimation for multiplicative cascades.
• Scaling exponents and multifractal dimensions for independent random cascades
• Inequalities for the $r$th Absolute Moment of a Sum of Random Variables, $1 \leqq r \leqq 2$
• Log-normal continuous cascade model of asset returns: aggregation properties and estimation