Measuring the roughness of random paths by increment ratios

DOI10.3150/10-BEJ291zbMath1248.60042arXiv0802.0489OpenAlexW2074028099MaRDI QIDQ453302

Donatas Surgailis, Jean-Marc Bardet

Publication date: 19 September 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.0489

zbMATH Keywords

Lévy processesfractional Brownian motiondiffusion processesmultifractional Brownian motionlimit theoremsHölder exponentestimation of the local regularity function of stochastic processtangent processzero crossings

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Strong limit theorems (60F15) Sample path properties (60G17)

Related Items (15)

The increment ratio statistic under deterministic trends ⋮ Local scaling limits of Lévy driven fractional random fields ⋮ Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size ⋮ Semiparametric stationarity and fractional unit roots tests based on data-driven multidimensional increment ratio statistics ⋮ CLT for quadratic variation of Gaussian processes and its application to the estimation of the Orey index ⋮ Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes ⋮ On a covariance structure of some subset of self-similar Gaussian processes ⋮ A short note on a class of statistics for estimation of the Hurst index of fractional Brownian motion ⋮ On comparison of the estimators of the Hurst index and the diffusion coefficient of the fractional Gompertz diffusion process ⋮ Cusum tests for changes in the Hurst exponent and volatility of fractional Brownian motion ⋮ An adaptive estimator of the memory parameter and the goodness-of-fit test using a multidimensional increment ratio statistic ⋮ An estimator of the tail index based on increment ratio statistics ⋮ Statistical Estimation for a Class of Self‐Regulating Processes ⋮ Exact uniform modulus of continuity and Chung's LIL for the generalized fractional Brownian motion ⋮ Parameter estimation for discretized geometric fractional Brownian motions with applications in Chinese financial markets

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