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

共 50 条

[31] Stochastic evolution equations in UMD Banach spaces
van Neerven, J. M. A. M.
Veraar, M. C.
Weis, L.
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (04) : 940 - 993
[32] Stochastic Dirichlet–Poisson Problem on Hilbert Spaces
Sonia Chaari
Afef Ben Farah
[J]. Complex Analysis and Operator Theory, 2024, 18
[33] PRODUCT INTEGRATION IN REFLEXIVE BANACH-SPACES
FITZGIBBON, WE
[J]. MONATSHEFTE FUR MATHEMATIK, 1977, 83 (02): : 113 - 119
[34] PRODUCT INTEGRATION IN REFLEXIVE BANACH-SPACES
FITZGIBBON, WE
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A189 - A189
[35] ON INTEGRATION IN BANACH-SPACES .6.
DOBRAKOV, I
MORALES, P
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 1985, 35 (02) : 173 - 187
[36] ASYMPTOTIC STRUCTURE OF BANACH SPACES AND RIEMANN INTEGRATION
Naralenkov, K. M.
[J]. REAL ANALYSIS EXCHANGE, 2007, 33 (01) : 111 - 124
[37] ON INTEGRATION IN BANACH-SPACES .7.
DOBRAKOV, I
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 1988, 38 (03) : 434 - 449
[38] Stochastic integration of functions with values in a Banach space
van Neerven, JMAM
Weis, L
[J]. STUDIA MATHEMATICA, 2005, 166 (02) : 131 - 170
[39] Symplectic leaves in real Banach Lie-Poisson spaces
Beltita, D
Ratiu, TS
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2005, 15 (04) : 753 - 779
[40] Induced and coinduced Banach Lie-Poisson spaces and integrability
Odzijewicz, Anatol
Ratiu, Tudor S.
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (05) : 1225 - 1272

← 1 2 3 4 5 →