Multivariate stochastic integrals with respect to independently scattered random measures on $\delta$-rings

@article{Kremer2019MultivariateSI,
  title={Multivariate stochastic integrals with respect to independently scattered random measures on \$\delta\$-rings},
  author={Dustin Kremer and Hans-Peter Scheffler},
  journal={Publicationes Mathematicae Debrecen},
  year={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 such a random measure, the class of all integrable matrix-valued deterministic functions is characterized in terms of certain characteristics of the random measure. In addition a general construction principle is presented. 
Multi operator-stable random measures and fields
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
Implicit max-stable extremal integrals
  • D. Kremer
  • Mathematics, Computer Science
    Extremes
  • 2020
TLDR
This paper solves an open problem in Goldbach (2016) by developing a stochastic integral of a deterministic function g ≥ 0 with respect to implicit max-stable sup-measures and reveals striking parallels in the construction ofmax-stable extremal integrals.
Operator-stable and operator-self-similar random fields

References

SHOWING 1-10 OF 22 REFERENCES
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
Stable random variables on the real line Multivariate stable distributions Stable stochastic integrals Dependence structures of multivariate stable distributions Non-linear regression Complex stable
Operator scaling stable random fields
Spectral representations of infinitely divisible processes
SummaryThe spectral representations for arbitrary discrete parameter infinitely divisible processes as well as for (centered) continuous parameter infinitely divisible processes, which are separable
Infinite divisibility of random fields admitting an integral representation with an infinitely divisible integrator
We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely
Lévy processes and infinitely divisible distributions
Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5.
Introduction to Tensor Products of Banach Spaces
This volume provides a self-contained introduction to the theory of tensor products of Banach spaces. It is written for graduate students in analysis or for researchers in other fields who wish to
Extension of multiplicative set functions with values in a Banach algebra
Let X be a given set, and let R, S be some classes of certain subsets of X. We say that R is a ring if A+B ∈ R, A−B ∈ R whenever A ∈ R, B ∈ R. We say that S is a σ-ring if it is a ring and if for
Linear Operators
Linear AnalysisMeasure and Integral, Banach and Hilbert Space, Linear Integral Equations. By Prof. Adriaan Cornelis Zaanen. (Bibliotheca Mathematica: a Series of Monographs on Pure and Applied
Pseudo-differential operators and Markov processes
On etudie l'existence et l'unicite des solutions du probleme de martingale pour une classe de generateurs de type Levy, non degeneres, dont les caracteristiques locales ne sont pas toujours continues
...
...