A fractional stochastic evolution equation driven by fractional Brownian motion

A singular stochastic differential equation driven by fractional Brownian motion∗

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.

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

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

Stochastic evolution equations with fractional Brownian motion

In this paper linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. A necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed; separate proofs are required for the cases of Hurst parameter above and below 1/2. The particular case of the Laplaci...

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...