Multivariate Operator-Self-Similar Random Fields

Abstract

Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are characterized. Two classes of operator-self-similar stable random fields $X=\{X(t),t\in {\mathbb{R}}^d\}$ with values in ${\mathbb{R}}^m$ are constructed by utilizing homogeneous functions and stochastic integral representations.

27 pages

References in corpus (2)

• Integral representations and properties of operator fractional Brownian motions
• Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes

Cited by in corpus (9)

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• Occupation Time Fluctuations of Weakly Degenerate Branching Systems
• The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields
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• Tangent fields, intrinsic stationarity, and self-similarity (with a supplement on Matheron Theory)
• Linear SPDEs with harmonizable noise
• Multi operator-stable random measures and fields
• Multi-scale Invariant Fields: Estimation and Prediction
• On integral representations of operator fractional Brownian fields