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
Operator-stable and operator-self-similar random fields
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.

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