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

Dustin Kremer; Hans-Peter Scheffler

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arXiv · 1711.00890

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

Dustin Kremer·Hans-Peter Scheffler

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Abstract

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.

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Dustin Kremer, Hans-Peter Scheffler. 2017-11-02. Multivariate stochastic integrals with respect to independently scattered random measures on {\delta}-rings. https://arxiv.org/abs/1711.00890

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