Averaging dynamics driven by fractional Brownian motion

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

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion

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

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.

Maxima of stochastic processes driven by fractional Brownian motion

We study stationary processes given as solutions to SDEs driven by fractional Brownian motion (FBM). This class includes the fractional Ornstein-Uhlenbeck process (FOUP), but is a much richer class of processes, which can be obtained by state space transformations of the FOUP. An explicit formula in terms of Euler’s Γ-function describes the asymptotic behaviour of the covariance function of FOU...