article Poisson stochastic integration in Banach spaces published Sjoerd Dirksen author Jan Maas author 4C5696CE-F248-11E8-B48F-1D18A9856A870000-0002-0845-1338 Jan Van Neerven author 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. Institute of Mathematical Statistics2013 Electronic Journal of Probability10.1214/EJP.v18-2945 18 yes Dirksen, S., Maas, J., &#38; Van Neerven, J. (2013). Poisson stochastic integration in Banach spaces. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/EJP.v18-2945 ">https://doi.org/10.1214/EJP.v18-2945 </a> Dirksen, Sjoerd, Jan Maas, and Jan Van Neerven. “Poisson Stochastic Integration in Banach Spaces.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2013. <a href="https://doi.org/10.1214/EJP.v18-2945 ">https://doi.org/10.1214/EJP.v18-2945 </a>. Dirksen, Sjoerd, et al. “Poisson Stochastic Integration in Banach Spaces.” <i>Electronic Journal of Probability</i>, vol. 18, Institute of Mathematical Statistics, 2013, doi:<a href="https://doi.org/10.1214/EJP.v18-2945 ">10.1214/EJP.v18-2945 </a>. Dirksen S, Maas J, Van Neerven J. Poisson stochastic integration in Banach spaces. <i>Electronic Journal of Probability</i>. 2013;18. doi:<a href="https://doi.org/10.1214/EJP.v18-2945 ">10.1214/EJP.v18-2945 </a> S. Dirksen, J. Maas, and J. Van Neerven, “Poisson stochastic integration in Banach spaces,” <i>Electronic Journal of Probability</i>, 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. S. Dirksen, J. Maas, J. Van Neerven, Electronic Journal of Probability 18 (2013). 21172018-12-11T11:55:49Z2021-01-12T06:55:24Z