Poisson stochastic integration in Banach spaces
Dirksen S, Maas J, Van Neerven J. 2013. Poisson stochastic integration in Banach spaces. Electronic Journal of Probability. 18.
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Dirksen, Sjoerd;
Maas, JanISTA 
;
van Neerven, Jan M
;
van Neerven, Jan MAbstract
We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non-trivial martingale (co)type and extend various results in the literature. We also develop a Malliavin framework to interpret Poisson stochastic integrals as vector-valued Skorohod integrals, and prove a Clark-Ocone representation formula.
Publishing Year
Date Published
2013-11-18
Journal Title
Electronic Journal of Probability
Acknowledgement
The first and third named authors were supported by VICI subsidy 639.033.604 of the Netherlands Organisation for Scientific Research (NWO). The first and second named authors were supported by the German Research Foundation in the Collaborative Research C
Volume
18
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Cite this
Dirksen S, Maas J, Van Neerven J. Poisson stochastic integration in Banach spaces. Electronic Journal of Probability. 2013;18. doi:10.1214/EJP.v18-2945
Dirksen, S., Maas, J., & Van Neerven, J. (2013). Poisson stochastic integration in Banach spaces. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v18-2945
Dirksen, Sjoerd, Jan Maas, and Jan Van Neerven. “Poisson Stochastic Integration in Banach Spaces.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2013. https://doi.org/10.1214/EJP.v18-2945 .
S. Dirksen, J. Maas, and J. Van Neerven, “Poisson stochastic integration in Banach spaces,” Electronic Journal of Probability, vol. 18. Institute of Mathematical Statistics, 2013.
Dirksen S, Maas J, Van Neerven J. 2013. Poisson stochastic integration in Banach spaces. Electronic Journal of Probability. 18.
Dirksen, Sjoerd, et al. “Poisson Stochastic Integration in Banach Spaces.” Electronic Journal of Probability, vol. 18, Institute of Mathematical Statistics, 2013, doi:10.1214/EJP.v18-2945 .
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