Stochastic Analysis of the Fractional Brownian Motion

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

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...

Control of Some Stochastic Systems with a Fractional Brownian Motion

Some stochastic control systems that are described by stochastic differential equations with a fractional Brownian motion are considered. The solutions of these systems are defined by weak solutions. These weak solutions are obtained by the transformation of the measure for a fractional Brownian motion by a Radon-Nikodym derivative. This weak solution approach is used to solve a control problem...

Stochastic Analysis of the Fractional BrownianMotionBy

Since the fractional Brownian motion is not a semiimartingale, the usual Ito calculus cannot be used to deene a full stochastic calculus. However, in this work, we obtain the Itt formula, the ItttClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.