Cylindrical fractional Brownian motion in Banach spaces

被引：5

作者：

Issoglio, E. ^{[1
]}

Riedle, M. ^{[1
]}

机构：

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

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2014年 / 124卷 / 11期

基金：

英国工程与自然科学研究理事会;

关键词：

Cylindrical fractional Brownian motion; Stochastic integration in Banach spaces; Stochastic partial differential equations; Fractional Ornstein-Uhlenbeck process; gamma-radonifying; Cylindrical measures; STOCHASTIC INTEGRATION; EVOLUTION-EQUATIONS; HILBERT-SPACE; CALCULUS; NOISES;

D O I：

10.1016/j.spa.2014.05.010

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：

In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of cylindrical random variables and cylindrical measures. The developed stochastic integral for deterministic operator valued integrands is based on a series representation of the cylindrical fractional Brownian motion, which is analogous to the Karhunen-Loeve expansion for genuine stochastic processes. In the last part we apply our results to study the abstract stochastic Cauchy problem in a Banach space driven by cylindrical fractional Brownian motion. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：3507 / 3534

页数：28

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