Operator-self-similar stable processes

DOI10.1016/0304-4149(94)00010-7zbMath0814.60032OpenAlexW2090912818MaRDI QIDQ1343600

J. David Mason, Makoto Maejima

Publication date: 13 June 1995

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

Full work available at URL: https://doi.org/10.1016/0304-4149(94)00010-7

zbMATH Keywords

operator fractional Brownian motionoperator-stable lawoperator-self-similar process

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Self-similar stochastic processes (60G18)

Related Items (26)

Spectral decomposition for operator self-similar processes and their generalized domains of attraction ⋮ Limit theorems related to a class of operator-self-similar processes ⋮ Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation ⋮ On operator fractional Lévy motion: integral representations and time-reversibility ⋮ Convergence in law to operator fractional Brownian motions ⋮ Operator self-similar processes and functional central limit theorems ⋮ Convergence in law to operator fractional Brownian motion of Riemann-Liouville type ⋮ Exponents, symmetry groups and classification of operator fractional Brownian motions ⋮ Wavelet eigenvalue regression in high dimensions ⋮ Integral representations and properties of operator fractional Brownian motions ⋮ Wavelet estimation in OFBM: choosing scale parameter in different sampling methods and different parameter values ⋮ Operator fractional Brownian motion and martingale differences ⋮ Hurst estimation for operator scaling random fields ⋮ On multivariate fractional random fields: tempering and operator-stable laws ⋮ On integral representations of operator fractional Brownian fields ⋮ Multivariate operator-self-similar random fields ⋮ A note on operator self-similar Gaussian vector fields ⋮ Operator semi-self-similar processes and their space-scaling matrices ⋮ Operator-stable and operator-self-similar random fields ⋮ Wavelet eigenvalue regression for \(n\)-variate operator fractional Brownian motion ⋮ On the probability distribution of the local times of diagonally operator-self-similar Gaussian fields with stationary increments ⋮ Some results about the sample path properties of Markov processes with independent self-similar components ⋮ AN INTRODUCTION TO THE THEORY OF SELF-SIMILAR STOCHASTIC PROCESSES ⋮ Two-step wavelet-based estimation for Gaussian mixed fractional processes ⋮ Covariance function of vector self-similar processes ⋮ Normalisers and centralisers of compact matrix groups. An elementary approach

Cites Work

• Operator stable laws: Series representations and domains of normal attraction
• Operator-stable laws
• Operator self similar stochastic processes in \(R^ n\).
• Self-similar processes with independent increments
• On a class of self-similar processes
• Operator-Self-Similar Processes in a Finite-Dimensional Space
• Semi-Stable Stochastic Processes
• Fractional Brownian Motions, Fractional Noises and Applications
• Operator-Stable Probability Distributions on Vector Groups
• The Invariance Principle for Stationary Processes
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