Poisson stochastic integration in Banach spaces

被引：13
|
作者：
Dirksen, Sjoerd [1 ]
Maas, Jan [2 ]
van Neerven, Jan [3 ]
机构：
[1] Univ Bonn, Inst Numer Simulat, Bonn, Germany
[2] Univ Bonn, Inst Appl Math, Bonn, Germany
[3] Delft Univ Technol, Delft Inst Appl Math, NL-2600 AA Delft, Netherlands
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2013年 / 18卷
关键词：
Stochastic integration; Poisson random measure; martingale type; UMD Banach spaces; stochastic convolutions; Malliavin calculus; Clark-Ocone representation theorem; MARTINGALE REPRESENTATION; INEQUALITIES; EQUATIONS; CALCULUS;
D O I：
10.1214/EJP.v18-2945
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
引用
收藏
页码：1 / 28
页数：28
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