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

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...

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.

Self-Similar Processes, Fractional Brownian Motion and Statistical Inference

Self-similar stochastic processes are used for stochastic modeling whenever it is expected that long range dependence may be present in the phenomenon under consideration. After discusing some basic concepts of self-similar processes and fractional Brownian motion, we review some recent work on parametric and nonparametric inference for estimation of parameters for linear systems of stochastic ...

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