---
_id: '2117'
abstract:
- lang: eng
text: 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.
acknowledgement: The first and third named authors were supported by VICI subsidy
639.033.604 of the Netherlands Organisation for Scientific Research (NWO). The first
and second named authors were supported by the German Research Foundation in the
Collaborative Research C
author:
- first_name: Sjoerd
full_name: Dirksen, Sjoerd
last_name: Dirksen
- first_name: Jan
full_name: Jan Maas
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Jan
full_name: van Neerven, Jan M
last_name: Van Neerven
citation:
ama: Dirksen S, Maas J, Van Neerven J. Poisson stochastic integration in Banach
spaces. Electronic Journal of Probability. 2013;18. doi:10.1214/EJP.v18-2945
apa: Dirksen, S., Maas, J., & Van Neerven, J. (2013). Poisson stochastic integration
in Banach spaces. Electronic Journal of Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/EJP.v18-2945
chicago: Dirksen, Sjoerd, Jan Maas, and Jan Van Neerven. “Poisson Stochastic Integration
in Banach Spaces.” Electronic Journal of Probability. Institute of Mathematical
Statistics, 2013. https://doi.org/10.1214/EJP.v18-2945
.
ieee: S. Dirksen, J. Maas, and J. Van Neerven, “Poisson stochastic integration in
Banach spaces,” Electronic Journal of Probability, vol. 18. Institute of
Mathematical Statistics, 2013.
ista: Dirksen S, Maas J, Van Neerven J. 2013. Poisson stochastic integration in
Banach spaces. Electronic Journal of Probability. 18.
mla: Dirksen, Sjoerd, et al. “Poisson Stochastic Integration in Banach Spaces.”
Electronic Journal of Probability, vol. 18, Institute of Mathematical Statistics,
2013, doi:10.1214/EJP.v18-2945
.
short: S. Dirksen, J. Maas, J. Van Neerven, Electronic Journal of Probability 18
(2013).
date_created: 2018-12-11T11:55:49Z
date_published: 2013-11-18T00:00:00Z
date_updated: 2021-01-12T06:55:24Z
day: '18'
doi: '10.1214/EJP.v18-2945 '
extern: 1
intvolume: ' 18'
main_file_link:
- open_access: '1'
url: 'http://arxiv.org/abs/1307.7901 '
month: '11'
oa: 1
publication: Electronic Journal of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '4917'
quality_controlled: 0
status: public
title: Poisson stochastic integration in Banach spaces
type: journal_article
volume: 18
year: '2013'
...