The Annals of Probability

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.

Article information

Source
Ann. Probab., Volume 42, Number 6 (2014), 2595-2643.

Dates
First available in Project Euclid: 30 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1412083633

Digital Object Identifier
doi:10.1214/13-AOP906

Mathematical Reviews number (MathSciNet)
MR3265175

Zentralblatt MATH identifier
1308.60068

Subjects
Primary: 60H05: Stochastic integrals
Secondary: 60H15: Stochastic partial differential equations [See also 35R60] 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 60G50: Sums of independent random variables; random walks 46L53: Noncommutative probability and statistics

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

Citation

Dirksen, Sjoerd. Itô isomorphisms for $L^{p}$-valued Poisson stochastic integrals. Ann. Probab. 42 (2014), no. 6, 2595--2643. doi:10.1214/13-AOP906. https://projecteuclid.org/euclid.aop/1412083633


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