Ornstein-Uhlenbeck Processes Driven by Cylindrical Levy Processes

被引：23

作者：

Riedle, Markus ^{[1
]}

机构：

[1] Kings Coll London, Dept Math, London WC2R 2LS, England

来源：

POTENTIAL ANALYSIS | 2015年 / 42卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Cylindrical Levy process; Stochastic integral; Stochastic integration; Stochastic evolution equation; Ornstein-Uhlenbeck process; TIME REGULARITY;

D O I：

10.1007/s11118-014-9458-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical L,vy processes in separable Banach spaces. Here, a cylindrical L,vy process is understood in the classical framework of cylindrical random variables and cylindrical measures, and thus, it can be considered as a natural generalisation of cylindrical Wiener processes or white noises. Depending on the underlying Banach space, we provide necessary and/or sufficient conditions for a function to be integrable. In the last part, the developed theory is applied to define Ornstein-Uhlenbeck processes driven by cylindrical L,vy processes and several examples are considered.

引用

页码：809 / 838

页数：30

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