A Law of Large Numbers for the Power Variation of Fractional Lévy Processes

DOI10.1080/07362994.2014.962045zbMath1316.60038OpenAlexW2052145782MaRDI QIDQ4981992

Sven Glaser

Publication date: 23 March 2015

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

Full work available at URL: http://hdl.handle.net/2003/30569

zbMATH Keywords

self-similaritylaw of large numbersinfinitely divisible distributions\(\alpha\)-stable processpower variationintegrated volatilityfractional Lévy processes

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Estimation in multivariate analysis (62H12) Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Strong limit theorems (60F15) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52)

Related Items (5)

Ambit Fields: Survey and New Challenges ⋮ Least squares estimator for Ornstein–Uhlenbeck processes driven by small fractional Lévy noises ⋮ Low-frequency estimation of continuous-time moving average Lévy processes ⋮ Parameter estimation for the discretely observed vasicek model with small fractional Lévy noise ⋮ On limit theory for functionals of stationary increments Lévy driven moving averages

Cites Work

• Unnamed Item
• On path properties of certain infinitely divisible processes
• Power variation of some integral fractional processes
• On roughness indices for fractional fields
• Fractional Lévy processes with an application to long memory moving average processes
• An inequality of the Hölder type, connected with Stieltjes integration
• Foundations of Modern Probability
• Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models
• A UNIFYING APPROACH TO FRACTIONAL LÉVY PROCESSES
• Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics

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