Stochastic integration for Levy processes with values in Banach spaces

被引：18

作者：

Riedle, Markus ^{[2
]}

van Gaans, Onno ^{[1
]}

机构：

[1] Leiden Univ, Inst Math, NL-2300 RA Leiden, Netherlands

[2] Univ Manchester, Manchester M13 9PL, Lancs, England

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2009年 / 119卷 / 06期

关键词：

Banach space valued stochastic integral; Cauchy problem; Levy-Ito decomposition; Levy process; Martingale valued measure; Pettis integral; Radonifying operator;

D O I：

10.1016/j.spa.2008.09.009

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：

A stochastic integral of Banach space valued deterministic functions with respect to Banach space valued Levy processes is defined. There are no conditions on the Banach spaces or on the Levy processes. The integral is defined analogously to the Pettis integral. The integrability of a function is characterized by means of a radonifying property of an integral operator associated with the integrand. The integral is used to prove a Levy-Ito decomposition for Banach space valued Levy processes and to Study existence and uniqueness of solutions of stochastic Cauchy problems driven by Levy processes. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：1952 / 1974

页数：23

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