Stochastic integration with respect to fractional Brownian motion

被引：10

作者：

Carmona, P ^{[1
]}

Coutin, L ^{[1
]}

机构：

[1] Univ Toulouse 3, Lab Stat & Probabil, F-31062 Toulouse 4, France

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 2000年 / 330卷 / 03期

关键词：

D O I：

10.1016/S0764-4442(00)00134-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to construct a stochastic integral with respect to fractional Brownian motion W-H, for every value of the Hurst index H is an element of (0, 1), as the limit of integrals with respect to semimartingales approximating W-H. We relate this construction to former integration theory (pathwise and stochastic), and in particular we give, for H > 1/4 a precise interpretation of Privault's Ito formula [12]. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

引用

页码：231 / 236

页数：6

共 13 条

[1]

ALOS E, 1999, MATH PREPRINT SERIES, V262

[2]

CARMONA P, 1998, 0698 U P SAB LAB STA

[3]

Dai W, 1996, J APPL MATH STOCHAST, V10, P439, DOI DOI 10.1155/S104895339600038X

[4]

DECREUSEFOND L, 1997, STOCHASTIC ANAL FRAC

[5]

DUDLEY RM, 1998, 1 U AARH CTR MATH PH

[6]

DUNCAN TE, 1998, STOCHASTIC CALCULUS, V1

[7]

Lebedev N.N., 1972, Dover Books on Math- ematics

[8] FUBINI THEOREM FOR ANTICIPATING STOCHASTIC INTEGRALS IN HILBERT-SPACE [J].

LEON, JA .

APPLIED MATHEMATICS AND OPTIMIZATION, 1993, 27 (03) :313-327

[9]

Lin S. J., 1995, STOCHASTICS STOCHAST, V55, P121

[10]

Nualart D., 1996, MALLIAVIN CALCULUS R, V71, P168

← 1 2 →