Stochastic calculus for fractional Brownian motion - I. Theory

被引：387

作者：

Duncan, TE ^{[1
]}

Hu, YZ ^{[1
]}

Pasik-Duncan, B ^{[1
]}

机构：

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2000年 / 38卷 / 02期

关键词：

fractional Brownian motion; stochastic calculus; Ito integral; Stratonovich integral; Ito formula; Wick product; Ito calculus; multiple Ito integrals; multiple Stratonovich integrals;

D O I：

10.1137/S036301299834171X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper a stochastic calculus is given for the fractional Brownian motions that have the Hurst parameter in (1/2, 1). A stochastic integral of Ito type is defined for a family of integrands so that the integral has zero mean and an explicit expression for the second moment. This integral uses the Wick product and a derivative in the path space. Some Ito formulae (or change of variables formulae) are given for smooth functions of a fractional Brownian motion or some processes related to a fractional Brownian motion. A stochastic integral of Stratonovich type is defined and the two types of stochastic integrals are explicitly related. A square integrable functional of a fractional Brownian motion is expressed as an infinite series of orthogonal multiple integrals.

引用

页码：582 / 612

页数：31