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

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