Open Access
November 2015 Integrability conditions for space–time stochastic integrals: Theory and applications
Carsten Chong, Claudia Klüppelberg
Bernoulli 21(4): 2190-2216 (November 2015). DOI: 10.3150/14-BEJ640


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.


Download Citation

Carsten Chong. Claudia Klüppelberg. "Integrability conditions for space–time stochastic integrals: Theory and applications." Bernoulli 21 (4) 2190 - 2216, November 2015.


Received: 1 March 2013; Revised: 1 March 2014; Published: November 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1333.60112
MathSciNet: MR3378464
Digital Object Identifier: 10.3150/14-BEJ640

Keywords: ambit process , continuous-time moving average , integrability conditions , Lévy basis , martingale measure , predictable characteristics , random measure , stochastic integration , Stochastic partial differential equation , supCARMA , supCOGARCH , supOU , Volterra process

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 4 • November 2015
Back to Top