A singular stochastic differential equation driven by fractional Brownian motion

被引：29

作者：

Hu, Yaozhong ^{[1
]}

Nualart, David ^{[1
]}

Song, Xiaoming ^{[1
]}

机构：

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

来源：

STATISTICS & PROBABILITY LETTERS | 2008年 / 78卷 / 14期

关键词：

D O I：

10.1016/j.spl.2008.01.080

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：

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter H > 1/2. Under some assumptions on the drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin calculus to prove that the solution has an absolutely continuous law at any time t > 0. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：2075 / 2085

页数：11

共 50 条

[1] Numerical method for singular drift stochastic differential equation driven by fractional Brownian motion
Zhou, Hao
Hu, Yaozhong
Zhao, Jingjun
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 447
[2] BACKWARD STOCHASTIC DIFFERENTIAL EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION
Hu, Yaozhong
Peng, Shige
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (03) : 1675 - 1700
[3] Modified Euler approximation of stochastic differential equation driven by Brownian motion and fractional Brownian motion
Liu, Weiguo
Luo, Jiaowan
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (15) : 7427 - 7443
[4] Controllability of a stochastic functional differential equation driven by a fractional Brownian motion
Jingqi Han
Litan Yan
Advances in Difference Equations, 2018
[5] Controllability of a stochastic functional differential equation driven by a fractional Brownian motion
Han, Jingqi
Yan, Litan
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[6] Parameter estimation in stochastic differential equation driven by fractional Brownian motion
Filatova, Daria
Grzywaczewski, Marek
Shybanova, Elizaveta
Zili, Mounir
EUROCON 2007: THE INTERNATIONAL CONFERENCE ON COMPUTER AS A TOOL, VOLS 1-6, 2007, : 2111 - 2117
[7] A Fractional Heston-Type Model as a Singular Stochastic Equation Driven by Fractional Brownian Motion
Mpanda, Marc Mukendi
FRACTAL AND FRACTIONAL, 2024, 8 (06)
[8] On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion
Jumarie, G
APPLIED MATHEMATICS LETTERS, 2005, 18 (07) : 817 - 826
[9] DETERMINISTIC CHARACTERIZATION OF VIABILITY FOR STOCHASTIC DIFFERENTIAL EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION
Nie, Tianyang
Rascanu, Aurel
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2012, 18 (04) : 915 - 929
[10] Stochastic fractional differential inclusion driven by fractional Brownian motion
Hachemi, Rahma Yasmina Moulay
Guendouzi, Toufik
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2023, 31 (04) : 303 - 313

← 1 2 3 4 5 →