Stochastic differential equations driven by fractional Brownian motion and Poisson point process

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

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...

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...

Parametric estimation for linear stochastic differential equations driven by fractional Brownian Motion

We investigate the asymptotic properties of the maximum likelihhod estimator and Bayes estimator of the drift parameter for stochastic processes satisfying a linear stochastic differential equations driven by fractional Brownian motion. We obtain a Bernstein-von Mises type theorem also for such a class of processes.

Weak Approximation of a Fractional Sde

Abstract. In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H ∈ (1/3, 1/2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in [4, 7], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in [13].