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arXiv · 1208.3885

Itô isomorphisms for $L^{p}$-valued Poisson stochastic integrals

Sjoerd Dirksen
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Abstract

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. 2014-10-28. Itô isomorphisms for $L^{p}$-valued Poisson stochastic integrals. https://doi.org/10.1214/13-aop906

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