Integrability conditions for space–time stochastic integrals: Theory and applications
Copyright policy )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.
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)
- Hong Kong Polytechnic University China (People's Republic of)
- Hong Kong University of Science and Technology (香港科技大學) China (People's Republic of)
Stochastic integrals, Stochastic partial differential equation, random measures, Random measure, Stochastic partial differential equations (aspects of stochastic analysis), continuous-time moving average, Integrability conditions, FOS: Mathematics, Lévy basis, SupOU, martingale measure, Ambit process, 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, SupCOGARCH, ambit processes, Probability (math.PR), space-time stochastic integrals, Stochastic integration, stochastic partial differential equation, Continuous-time moving average, ambit process, supOU, Predictable characteristics, supCOGARCH, integrability conditions, stochastic integration, Volterra process, SupCARMA, Martingale measure, predictable characteristics, supCARMA, random measure, Mathematics - Probability, Random measures, ddc: ddc:
Stochastic integrals, Stochastic partial differential equation, random measures, Random measure, Stochastic partial differential equations (aspects of stochastic analysis), continuous-time moving average, Integrability conditions, FOS: Mathematics, Lévy basis, SupOU, martingale measure, Ambit process, 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, SupCOGARCH, ambit processes, Probability (math.PR), space-time stochastic integrals, Stochastic integration, stochastic partial differential equation, Continuous-time moving average, ambit process, supOU, Predictable characteristics, supCOGARCH, integrability conditions, stochastic integration, Volterra process, SupCARMA, Martingale measure, predictable characteristics, supCARMA, random measure, Mathematics - Probability, Random measures, ddc: ddc:
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