Stochastic calculus for fractional Brownian motion - I. Theory

被引:377
|
作者
Duncan, TE [1 ]
Hu, YZ [1 ]
Pasik-Duncan, B [1 ]
机构
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
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
收藏
页码:582 / 612
页数:31
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