Corinne Berzin

Estimation in models driven by fractional Brownian motion

Let

Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion

\{b_H(t),t\in\mathbb{R}\}

Convergence of non-linear functionals of smoothed empirical processes and kernel density estimates

be the fractional Brownian motion with parameter

Variance estimator for fractional diffusions with variance and drift depending on time

0<H<1

Estimation of the Parameters

. When

Simulation Algorithms and Simulation Studies

1/2<H

Some Pascal Procedures and Functions

, we consider diffusion equations of the type \[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm {d}u.\] In different particular models where

Tables and Figures Related to the Simulation Studies

\sigma(x)=\sigma

Proofs of All the Results

or

Estimating the Hurst Parameter

\sigma(x)=\sigma x