Numerical Implementation of Stochastic Operational Matrix Driven by a Fractional Brownian Motion for Solving a Stochastic Differential Equation

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.

Numerical implementation a stochastic operational matrix for solving a nonlinear backward stochastic differential equation

In this paper, a computational technique is proposed for solving a nonlinear backward stochastic differential equation involving standard Brownian motion. The method is presented via the block pulse functions in combination with the collocation method. With using this approach, the nonlinear backward stochastic differential is reduced to a stochastic nonlinear system of 2m equations and 2m unkn...

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...

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