Bernoulli

  • Bernoulli
  • Volume 21, Number 4 (2015), 2190-2216.

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

Carsten Chong and Claudia Klüppelberg

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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.

Article information

Source
Bernoulli, Volume 21, Number 4 (2015), 2190-2216.

Dates
Received: March 2013
Revised: March 2014
First available in Project Euclid: 5 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1438777591

Digital Object Identifier
doi:10.3150/14-BEJ640

Mathematical Reviews number (MathSciNet)
MR3378464

Zentralblatt MATH identifier
1333.60112

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

Citation

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


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