Some Properties of Fractional Bessel Processes Driven by Fractional Brownian Motion

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

Some Processes Associated with Fractional Bessel Processes

Let B = {(B1 t , . . . , Bd t ) , t ≥ 0} be a d-dimensional fractional Brownian motion with Hurst parameter H and let Rt = √ (B1 t ) 2 + · · · + (Bd t )2 be the fractional Bessel process. Itô’s formula for the fractional Brownian motion leads to the equation Rt = ∑d i=1 ∫ t 0 Bi s Rs dBi s + H(d − 1) ∫ t 0 s2H−1 Rs ds . In the Brownian motion case (H = 1/2), Xt = ∑d i=1 ∫ t 0 Bi s Rs dBi s is a...

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 ...

Stochastic Differential Equations Driven by a Fractional Brownian Motion

We study existence, uniqueness and regularity of some sto-chastic diierential equations driven by a fractional Brownian motion of any Hurst index H 2 (0; 1): 1. Introduction Fractional Brownian motion and other longgrange dependent processes are more and more studied because of their potential applications in several elds like telecommunications networks, nance markets, biology and so on The ma...