Stochastic integration for fractional Brownian motion in a Hilbert space

被引：40
作者：
Duncan, TE [1 ]
Jakubowski, J
Pasik-Duncan, B
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
[2] Univ Warsaw, Inst Math, PL-02097 Warsaw, Poland
来源：
STOCHASTICS AND DYNAMICS | 2006年 / 6卷 / 01期
基金：
美国国家科学基金会;
关键词：
fractional Brownian motion in a Hilbert space; stochastic calculus for a fractional; Brownian motion; stochastic integration in a Hilbert space; stochastic equations in a Hilbert space;
D O I：
10.1142/S0219493706001645
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 Hilbert space-valued stochastic integration is defined for an integrator that is a cylindrical fractional Brownian motion in a Hilbert space and an operator-valued integrand. Since the integrator is not a semimartingale for the fractional Brownian motions that are considered, a different definition of integration is required. Both deterministic and stochastic operator-valued integrands are used. The approach uses some ideas from Malliavin calculus. In addition to the definition of stochastic integration, an Ito formula is given for smooth functions of some processes that are obtained by the stochastic integration.
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收藏
页码：53 / 75
页数：23
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