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Poisson stochastic integration in Banach spaces. (English) Zbl 1285.60049
Summary: 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.

MSC:
60H05 Stochastic integrals
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60H07 Stochastic calculus of variations and the Malliavin calculus
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