Impulsive neutral functional differential equations driven by a fractional Brownian motion with unbounded delay

Functional differential equations driven by a fractional Brownian motion

In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by a fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), in a separable real Hilbert space. We prove an existence and uniqueness result of mild solution by means of the Banach fixed point principle. A practical example is provided to illustrate the viabil...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Stochastic Differential Equations Driven by a Fractional Brownian Motion

We study existence, uniqueness and regularity of some sto-chastic diierential equations driven by a fractional Brownian motion of any Hurst index H 2 (0; 1): 1. Introduction Fractional Brownian motion and other longgrange dependent processes are more and more studied because of their potential applications in several elds like telecommunications networks, nance markets, biology and so on The ma...

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Flow properties of differential equations driven by fractional Brownian motion

We prove that solutions of stochastic differential equations driven by fractional Brownian motion for H > 1/2 define flows of homeomorphisms on R. AMS Subject Classification: 60H05, 60H07