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

Chong, C.; Klüppelberg, C.

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Document type:

Zeitschriftenaufsatz

Author(s):

Chong, C. and Klüppelberg, C.

Title:

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 proce... »

Keywords:

ambit process, continuous-time moving average, integrability conditions, L\'evy basis, martingale measure, predictable characteristics, random measure, stochastic integration, stochastic partial differential equation, supCARMA, supCOGARCH, supOU, Volterra process

Journal title:

Bernoulli

Year:

2015

Journal volume:

Journal issue:

Pages contribution:

2190-2216

Reviewed:

Language:

Fulltext / DOI:

doi:10.3150/14-BEJ640