Electronic Journal of Probability

Poisson stochastic integration in Banach spaces

Sjoerd Dirksen, Jan Maas, and Jan Neerven

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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.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 100, 28 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H05: Stochastic integrals
Secondary: 60G55: Point processes 60H07: Stochastic calculus of variations and the Malliavin calculus

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

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Dirksen, Sjoerd; Maas, Jan; Neerven, Jan. Poisson stochastic integration in Banach spaces. Electron. J. Probab. 18 (2013), paper no. 100, 28 pp. doi:10.1214/EJP.v18-2945. https://projecteuclid.org/euclid.ejp/1465064325

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