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.

In this paper we describe the fundamental solution of the equation that is obtained linearizing the Uehling-Uhlenbeck equation around the steady state of Kolmogorov type f(k) = k−7/6. Detailed estimates on its asymptotics are obtained.

Abstract— This paper derives two discrete motion models for 3D pose recovery starting from the stochastic differential equations that describe the object’s motion in continuous time. The velocity is considered first as a Wiener process, which underlies the very often-used constant velocity model, and second as an Ornstein-Uhlenbeck process. Analysis of the autocorrelation signal derived in expe...

Also, a process {Yt : t ≥ 0} is said to have independent increments if, for all t0 < t1 < . . . < tn, the n random variables Yt1 − Yt0 , Yt2 − Yt1 , ..., Ytn − Ytn−1 are independent. This condition implies that {Yt : t ≥ 0} is Markovian, but not conversely. The increments are further said to be stationary if, for any t > s and h > 0, the distribution of Yt+h− Ys+h is the same as the distributio...

The talk will describe Ornstein-Uhlenbeck semigroups and explore an example in infinite dimensions related to the renormalization group of quantum field theory. An Ornstein-Uhlenbeck semigroup describes a diffusion process with constant diffusion and linear drift. The resulting effect is Gaussian convolution followed by rescaling. The first goal of the talk is to contrast the situation of detai...

We give a multivariate generalization of Borell’s noise stability theorem for Gaussian vectors. As a consequence we recover two inequalities, also due to Borell, for exit times of the Ornstein-Uhlenbeck process.