Integrability conditions for space-time stochastic integrals: Theory and applications

TL;DR

This paper establishes explicit integrability conditions for space-time stochastic integrals driven by random measures, extending temporal results and applying to complex models like ambit processes.

Contribution

It introduces a canonical decomposition for random measures in space-time, enabling explicit integrability criteria and broadening the scope of stochastic integral analysis.

Findings

Derived explicit integrability conditions for space-time stochastic integrals.

Extended the canonical decomposition to space-time random measures.

Applied results to ambit processes and other models.

Abstract

We derive explicit integrability conditions for stochastic integrals taken over time and space driven by a random measure. Our main tool is a canonical decomposition of a random measure which extends the results from the purely temporal case. We show that the characteristics of this decomposition can be chosen as predictable strict random measures, and we compute the characteristics of the stochastic integral process. We apply our conditions to a variety of examples, in particular to ambit processes, which represent a rich model class.