Self-Similarity and Lamperti Transformation for Random Fields

DOI10.1080/15326340701471018zbMath1125.60046OpenAlexW1995654147MaRDI QIDQ5421582

Murad S. Taqqu, Marc G. Genton, Olivier Perrin

Publication date: 24 October 2007

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: http://publications.ut-capitole.fr/2302/1/taqqu_2302.pdf

zbMATH Keywords

reducibilityself-similarityrandom fieldlocal stationarityfractional Brownian sheetLamperti transformationLévy fractional Brownian random field

Mathematics Subject Classification ID

Random fields (60G60) Self-similar stochastic processes (60G18)

Related Items (17)

Testing self-similarity through Lamperti transformations ⋮ Some remarks on definitions of memory for stationary random processes and fields ⋮ Wavelet series representation and geometric properties of harmonizable fractional stable sheets ⋮ Aggregation of network traffic and anisotropic scaling of random fields ⋮ Local scaling limits of Lévy driven fractional random fields ⋮ Lamperti-Type Theorems for Random Fields ⋮ Sample Paths Properties of the Set-Indexed Fractional Brownian Motion ⋮ Scaling transition and edge effects for negatively dependent linear random fields on \(\mathbb{Z}^2\) ⋮ On the Lamperti transform of the fractional Brownian sheet ⋮ Stationary and multi-self-similar random fields with stochastic volatility ⋮ Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure ⋮ Anisotropic scaling limits of long-range dependent random fields ⋮ Gaussian multi-self-similar random fields with distinct stationary properties of their rectangular increments ⋮ Probability distributions of extremes of self-similar Gaussian random fields ⋮ Multi-scale invariant fields: estimation and prediction ⋮ Example of a Gaussian Self-Similar Field With Stationary Rectangular Increments That Is Not a Fractional Brownian Sheet ⋮ Estimation of hurst parameter and minimum variance spectrum

Uses Software

• longmemo

Cites Work

• Stationary covariances associated with exponentially convex functions
• Reducing non-stationary random fields to stationarity and isotropy using a space deformation
• Fractional Brownian sheet
• Reducing non-stationary stochastic processes to stationarity by a time deformation
• On a time deformation reducing nonstationary stochastic processes to local stationarity
• On Convergence of Stochastic Processes
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