An Averaging Principle for Stochastic Differential Delay Equations with 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...

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

Stochastic evolution equations with fractional Brownian motion

In this paper linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. A necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed; separate proofs are required for the cases of Hurst parameter above and below 1/2. The particular case of the Laplaci...

Parametric Estimation for Linear Stochastic Delay Differential Equations Driven by Fractional Brownian Motion

Consider a linear stochastic differential equation dX(t) = (aX(t) + bX(t− 1))dt+ dW t , t ≥ 0 with time delay driven by a fractional Brownian motion {WH t , t ≥ 0}. We investigate the asymptotic properties of the maximum likelihood estimator of the parameter θ = (a, b).

Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion

We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter H ∈ (0, 1). A general framework is constructed to make precise the notions of “invariant measure” and “stationary state” for such a system. We then prove under rather weak dissipativity conditions that such an SDE possesses a unique st...