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

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.

Published at http://dx.doi.org/10.3150/14-BEJ640 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (4)

• Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes
• Multivariate supOU processes
• Superposition of COGARCH processes
• Implied Volatility Surface: Construction Methodologies and Characteristics

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• Simulation of stochastic Volterra equations driven by space--time Lévy noise
• Hybrid simulation scheme for volatility modulated moving average fields
• Stochastic wave equation with heavy-tailed noise: Uniqueness of solutions and past light-cone property
• The compact support property for solutions to stochastic heat equations with stable noise
• A Malliavin-Skorohod calculus in $L^0$ and $L^1$ for additive and Volterra-type processes