Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motion

被引：11

作者：

Boufoussi, Brahim ^{[1
]}

Hajji, Salah ^{[2
]}

机构：

[1] Cadi Ayyad Univ, Fac Sci Semlalia, Dept Math, Marrakech 2390, Morocco

[2] Reg Ctr Profess Educ & Training, Dept Math, Marrakech, Morocco

来源：

STATISTICS & PROBABILITY LETTERS | 2017年 / 129卷

关键词：

Mild solution; Semigroup of bounded linear operator; Fractional Brownian motion; Stochastic integration for fractional Brownian motion; EVOLUTION-EQUATIONS;

D O I：

10.1016/j.spl.2017.06.006

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 prove an existence and uniqueness result of mild solution for a stochastic delay differential equation in a Hilbert space driven by a fractional Brownian motion with the Hurst parameter H > 1/2 and with a non-deterministic diffusion coefficient. We also prove under a sufficient condition that the law of the norm of the solution admits a density with respect to Lebesgue measure on R. Published by Elsevier B.V.

引用

页码：222 / 229

页数：8

共 50 条

[31] EXISTENCE AND UNIQUENESS OF MILD SOLUTIONS TO NEUTRAL IMPULSIVE FRACTIONAL STOCHASTIC DELAY DIFFERENTIAL EQUATIONS DRIVEN BY BOTH BROWNIAN MOTION AND FRACTIONAL BROWNIAN MOTION
Ahmed, A. M. Sayed
DIFFERENTIAL EQUATIONS & APPLICATIONS, 2022, 14 (03): : 433 - 446
[32] Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion
Saussereau, Bruno
BERNOULLI, 2012, 18 (01) : 1 - 23
[33] Reflected stochastic differential equations driven by standard and fractional Brownian motion
Chadad, Monir
Erraoui, Mohamed
STOCHASTICS AND DYNAMICS, 2024, 24 (02)
[34] Mutual information for stochastic differential equations driven by fractional Brownian motion
Es-Sebaiy, Khalifa
Ouknine, Youssef
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2010, 18 (01) : 1 - 9
[35] Anticipative backward stochastic differential equations driven by fractional Brownian motion
Wen, Jiaqiang
Shi, Yufeng
STATISTICS & PROBABILITY LETTERS, 2017, 122 : 118 - 127
[36] Lyapunov Techniques for Stochastic Differential Equations Driven by Fractional Brownian Motion
Zeng, Caibin
Yang, Qigui
Chen, YangQuan
ABSTRACT AND APPLIED ANALYSIS, 2014,
[37] Weak solutions to stochastic differential equations driven by fractional brownian motion
Snuparkova, J.
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2009, 59 (04) : 879 - 907
[38] A Support Theorem for Stochastic Differential Equations Driven by a Fractional Brownian Motion
Xu, Jie
Sun, Yanhua
Ren, Jie
JOURNAL OF THEORETICAL PROBABILITY, 2023, 36 (02) : 728 - 761
[39] Asymptotic inference for stochastic differential equations driven by fractional Brownian motion
Shohei Nakajima
Yasutaka Shimizu
Japanese Journal of Statistics and Data Science, 2023, 6 : 431 - 455
[40] Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion
Nualart, David
Saussereau, Bruno
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (02) : 391 - 409

← 1 2 3 4 5 →