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Poisson stochastic integration in Banach spaces


 
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1. Title Title of document Poisson stochastic integration in Banach spaces
 
2. Creator Author's name, affiliation, country Sjoerd Dirksen; University of Bonn; Germany
 
2. Creator Author's name, affiliation, country Jan Maas; University of Bonn; Germany
 
2. Creator Author's name, affiliation, country Jan van Neerven; Delft University of Technology; Netherlands
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stochastic integration, Poisson random measure, martingale type, UMD Banach spaces, stochastic convolutions, Malliavin calculus, Clark-Ocone representation theorem.
 
3. Subject Subject classification Primary 60H05; Secondary: 60G55, 60H07.
 
4. Description Abstract

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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) German Research Foundation (DFG), Netherlands Organisation for Scientific Research (NWO)
 
7. Date (YYYY-MM-DD) 2013-11-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2945
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2945
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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