Multi operator-stable random measures and fields

@article{Kremer2019MultiOR,
title={Multi operator-stable random measures and fields},
author={Dustin Kremer and Hans-Peter Scheffler},
journal={Stochastic Models},
year={2019},
volume={35},
pages={429 - 468}
}
• Published 28 September 2018
• Mathematics
• Stochastic Models
Abstract In this paper we construct vector-valued multi operator-stable random measures that behave locally like operator-stable random measures. The space of integrable functions is characterized in terms of a certain quasi-norm. Moreover, a multi operator-stable moving-average representation of a random field is presented which behaves locally like an operator-stable random field which is also operator-self-similar.
3 Citations

References

SHOWING 1-10 OF 30 REFERENCES
Operator-stable and operator-self-similar random fields
• Mathematics
Stochastic Processes and their Applications
• 2019
Multivariate stochastic integrals with respect to independently scattered random measures on $\delta$-rings
• Mathematics
Publicationes Mathematicae Debrecen
• 2019
In this paper we construct general vector-valued infinite-divisible independently scattered random measures with values in $\mathbb{R}^m$ and their corresponding stochastic integrals. Moreover, given
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
• Mathematics
• 1995
Stable random variables on the real line Multivariate stable distributions Stable stochastic integrals Dependence structures of multivariate stable distributions Non-linear regression Complex stable
Multistable Processes and Localizability
• Mathematics
• 2010
We use characteristic functions to construct α-multistable measures and integrals, where the measures behave locally like stable measures, but with the stability index α(t) varying with t. This
Exact moduli of continuity for operator-scaling Gaussian random fields
• Mathematics
• 2015
Let $X=\{X(t),t\in\mathrm{R}^N\}$ be a centered real-valued operator-scaling Gaussian random field with stationary increments, introduced by Bierm\'{e}, Meerschaert and Scheffler (Stochastic Process.
Operator-limit distributions in probability theory
• Mathematics
• 1993
Preliminaries Convergence of Types Theorems, Symmetry Groups, and Decomposability Semigroups Operator-Self-decomposable Measures Operator-Stable Measures.
Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice
• Mathematics
• 2001
Preface. Acknowledgments. INTRODUCTION. Random Vectors. Linear Operators. Infinitely Divisible Distributions and Triangular Arrays. MULTIVARIATE REGULAR VARIATION. Regular Variations for Linear
Real Analysis and Probability
1. Foundations: set theory 2. General topology 3. Measures 4. Integration 5. Lp spaces: introduction to functional analysis 6. Convex sets and duality of normed spaces 7. Measure, topology, and