A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion

Milstein’s type schemes for fractional SDEs

E|Bt −Bs| = cp|t− s| , s, t ∈ [0, 1], with cp = E(|G|), G ∼ N (0, 1), and, consequently, almost all sample paths of B are Hölder continuous of any order α ∈ (0,H). The study of stochastic differential equations driven by B has been considered by using several methods. For instance, in [22] one uses fractional calculus of same type as in [25]; in [2] one uses rough paths theory introduced in [11...

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

A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one

In this paper, we will focus in dimension one on the SDEs of the type dXt = σ(Xt)dB H t + b(Xt)dt where B H is a fractional Brownian motion. Our principal motivation is to describe one of the simplest theory from our point of view allowing to study this SDE, and this for any H ∈ (0, 1). We will consider several definitions of solution and we will study, for each one of them, in which condition ...

Operators Associated with a Stochastic Differential Equation Driven by Fractional Brownian Motions

In this paper, by using a Taylor development type formula, we show how it is possible to associate differential operators with stochastic differential equations driven by a fractional Brownian motion. As an application, we deduce that invariant measures for such SDEs must satisfy an infinite dimensional system of partial differential equations.

The Rate of Convergence of Euler Approximations for Solutions of Stochastic Differential Equations Driven by Fractional Brownian Motion

The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index H > 1/2 can be estimated by O(δ) (δ is the diameter of partition). For discrete-time approximations of Sko...