--- _id: '2117' abstract: - lang: eng text: 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. 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 author: - first_name: Sjoerd full_name: Dirksen, Sjoerd last_name: Dirksen - first_name: Jan full_name: Jan Maas id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Jan full_name: van Neerven, Jan M last_name: Van Neerven citation: ama: 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 apa: 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 chicago: 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 . ieee: 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. ista: Dirksen S, Maas J, Van Neerven J. 2013. Poisson stochastic integration in Banach spaces. Electronic Journal of Probability. 18. mla: 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 . short: S. Dirksen, J. Maas, J. Van Neerven, Electronic Journal of Probability 18 (2013). date_created: 2018-12-11T11:55:49Z date_published: 2013-11-18T00:00:00Z date_updated: 2021-01-12T06:55:24Z day: '18' doi: '10.1214/EJP.v18-2945 ' extern: 1 intvolume: ' 18' main_file_link: - open_access: '1' url: 'http://arxiv.org/abs/1307.7901 ' month: '11' oa: 1 publication: Electronic Journal of Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '4917' quality_controlled: 0 status: public title: Poisson stochastic integration in Banach spaces type: journal_article volume: 18 year: '2013' ...