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

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

A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions

We study the stability of the solutions of stochastic differential equations driven by fractional Brownian motions with Hurst parameter greater than half. We prove that when the initial conditions, the drift, and the diffusion coefficients as well as the fractional Brownian motions converge in a suitable sense, then the sequence of the solutions of the corresponding equations converge in Hölder...

Title Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H > 1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential eq...

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

Taylor expansion for the solution of a stochastic differential equation driven by fractional Brownian motions

We study the Taylor expansion for the solution of a differential equation driven by a multi-dimensional Hölder path with exponent β > 1/2. We derive a convergence criterion that enables us to write the solution as an infinite sum of iterated integrals on a nonempty interval. We apply our deterministic results to stochastic differential equations driven by fractional Brownian motions with Hurst ...