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November 2014 Itô isomorphisms for $L^{p}$-valued Poisson stochastic integrals
Sjoerd Dirksen
Ann. Probab. 42(6): 2595-2643 (November 2014). DOI: 10.1214/13-AOP906


Motivated by the study of existence, uniqueness and regularity of solutions to stochastic partial differential equations driven by jump noise, we prove Itô isomorphisms for $L^{p}$-valued stochastic integrals with respect to a compensated Poisson random measure. The principal ingredients for the proof are novel Rosenthal type inequalities for independent random variables taking values in a (noncommutative) $L^{p}$-space, which may be of independent interest. As a by-product of our proof, we observe some moment estimates for the operator norm of a sum of independent random matrices.


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Sjoerd Dirksen. "Itô isomorphisms for $L^{p}$-valued Poisson stochastic integrals." Ann. Probab. 42 (6) 2595 - 2643, November 2014.


Published: November 2014
First available in Project Euclid: 30 September 2014

zbMATH: 1308.60068
MathSciNet: MR3265175
Digital Object Identifier: 10.1214/13-AOP906

Primary: 60H05
Secondary: 46L53 , 60B20 , 60G50 , 60H15

Keywords: Decoupling inequalities , noncommutative $L^{p}$-spaces , norm estimates for random matrices , Poisson stochastic integration in Banach spaces , vector-valued Rosenthal inequalities

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 6 • November 2014
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