Fractional differential equations under stochastic input processes handled by the improved pseudo-force approach

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

Fractional Lévy driven Ornstein-Uhlenbeck processes and stochastic differential equations

Using Riemann-Stieltjes methods for integrators of bounded p-variation we define a pathwise integral driven by a fractional Lévy process (FLP). To explicitly solve general fractional stochastic differential equations (SDEs) we introduce an Ornstein-Uhlenbeck model by a stochastic integral representation, where the driving stochastic process is an FLP. To achieve the convergence of improper inte...

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

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...