Stochastic differential equations for fractional Brownian motions

被引：20

作者：

Coutin, L ^{[1
]}

Qian, ZM ^{[1
]}

机构：

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

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 2000年 / 331卷 / 01期

关键词：

D O I：

10.1016/S0764-4442(00)01594-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct via dyadic approximations a canonical geometric rough path in the sense of [7] associated to a fractional Brownian motion with Hurst parameter h, h epsilon]1/4, 1/2[. Therefore, we obtain a Wong-Zakai type approximation theorem for solutions of stochastic differential equations driven by these fractional Brownian motions. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

引用

页码：75 / 80

页数：6

共 50 条

[1] Stochastic differential equations driven by fractional Brownian motions
Jien, Yu-Juan
Ma, Jin
[J]. BERNOULLI, 2009, 15 (03) : 846 - 870
[2] Local times of stochastic differential equations driven by fractional Brownian motions
Lou, Shuwen
Ouyang, Cheng
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2017, 127 (11) : 3643 - 3660
[3] Properties of solutions of stochastic differential equations with standard and fractional Brownian motions
Levakov, A. A.
Vas'kovskii, M. M.
[J]. DIFFERENTIAL EQUATIONS, 2016, 52 (08) : 972 - 980
[4] Properties of solutions of stochastic differential equations with standard and fractional Brownian motions
A. A. Levakov
M. M. Vas’kovskii
[J]. Differential Equations, 2016, 52 : 972 - 980
[5] Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions
Arhrrabi, Elhoussain
Elomari, M'hamed
Melliani, Said
Chadli, Lalla Saadia
[J]. ADVANCES IN FUZZY SYSTEMS, 2021, 2021
[6] Stability of Linear Stochastic Differential Equations of Mixed Type with Fractional Brownian Motions
I. V. Kachan
[J]. Differential Equations, 2021, 57 : 570 - 586
[7] Stability of Linear Stochastic Differential Equations of Mixed Type with Fractional Brownian Motions
Kachan, I., V
[J]. DIFFERENTIAL EQUATIONS, 2021, 57 (05) : 570 - 586
[8] Stability and Attraction of Solutions of Nonlinear Stochastic Differential Equations with Standard and Fractional Brownian Motions
Vas'kovskii, M. M.
[J]. DIFFERENTIAL EQUATIONS, 2017, 53 (02) : 157 - 170
[9] Stability and attraction of solutions of nonlinear stochastic differential equations with standard and fractional Brownian motions
M. M. Vas’kovskii
[J]. Differential Equations, 2017, 53 : 157 - 170
[10] Upper bounds for the density of solutions to stochastic differential equations driven by fractional Brownian motions
Baudoin, Fabrice
Ouyang, Cheng
Tindel, Samy
[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2014, 50 (01): : 111 - 135

← 1 2 3 4 5 →