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

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.

Parameter estimation for nonergodic Ornstein-Uhlenbeck process driven by the weighted fractional Brownian motion

Distributions of the Maximum Likelihood and Minimum Contrast Estimators Associated with the Fractional Ornstein-Uhlenbeck Process

We discuss some inference problems associated with the fractional Ornstein-Uhlenbeck (fO-U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter H is known and is in [1/2, 1). Under this setting we compute the distributions of the maximum likelihood estimator (MLE) and the minimum co...

Parameter estimation for fractional Ornstein-Uhlenbeck processes

We study a least squares estimator b θT for the Ornstein-Uhlenbeck process, dXt = θXtdt+σdB H t , driven by fractional Brownian motion B H with Hurst parameter H ≥ 1 2 . We prove the strong consistence of b θT (the almost surely convergence of b θT to the true parameter θ). We also obtain the rate of this convergence when 1/2 ≤ H < 3/4, applying a central limit theorem for multiple Wiener integ...

High-resolution product quantization for Gaussian processes under sup-norm distortion

We derive high-resolution upper bounds for optimal product quantization of pathwise contionuous Gaussian processes respective to the supremum norm on [0, T ]. Moreover, we describe a product quantization design which attains this bound. This is achieved under very general assumptions on random series expansions of the process. It turns out that product quantization is asymptotically only slight...