- Volume 21, Number 4 (2015), 2190-2216.
Integrability conditions for space–time stochastic integrals: Theory and applications
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.
Bernoulli, Volume 21, Number 4 (2015), 2190-2216.
Received: March 2013
Revised: March 2014
First available in Project Euclid: 5 August 2015
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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
Chong, Carsten; Klüppelberg, Claudia. Integrability conditions for space–time stochastic integrals: Theory and applications. Bernoulli 21 (2015), no. 4, 2190--2216. doi:10.3150/14-BEJ640. https://projecteuclid.org/euclid.bj/1438777591