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

页码：1 / 28

页数：28

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