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2013 Poisson stochastic integration in Banach spaces
Sjoerd Dirksen, Jan Maas, Jan Neerven
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Electron. J. Probab. 18: 1-28 (2013). DOI: 10.1214/EJP.v18-2945


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.


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Sjoerd Dirksen. Jan Maas. Jan Neerven. "Poisson stochastic integration in Banach spaces." Electron. J. Probab. 18 1 - 28, 2013.


Accepted: 18 November 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1285.60049
MathSciNet: MR3141801
Digital Object Identifier: 10.1214/EJP.v18-2945

Primary: 60H05
Secondary: 60G55 , 60H07

Keywords: Clark-Ocone representation theorem , Malliavin calculus , martingale type , Poisson random measure , stochastic convolutions , stochastic integration , UMD Banach spaces

Vol.18 • 2013
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