Estimation of the drift of fractional Brownian motion

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

Drift Parameter Estimation for a Reflected Fractional Brownian Motion Based on its Local Time

We consider a drift parameter estimation problem when the state process is a reflected fractional Brownian motion (RFBM) with a nonzero drift parameter and the observation is the associated local time process. The RFBM process arises as the key approximating process for queueing systems with long range dependent and self similar input processes, where the drift parameter carries the physical me...

Minimum L1-norm Estimation for Fractional Ornstein-Uhlenbeck Type Process

We investigate the asymptotic properties of the minimum L1-norm estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process satisfying a linear stochastic differential equation driven by a fractional Brownian motion.

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

Sequential Estimation for Fractional Ornstein-Uhlenbeck Type Process

We investigate the asymptotic properties of the sequential maximum likelihhod estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process satisfying a linear stochastic differential equation driven by fractional Brownian motion.