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.
"Poisson stochastic integration in Banach spaces." Electron. J. Probab. 18 1 - 28, 2013. https://doi.org/10.1214/EJP.v18-2945