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...

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...

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.

Given a probability density, we estimate the rate of decay of the measure of the level sets of its evolutes by the Ornstein-Uhlenbeck semigroup. It is faster than what follows from the preservation of mass and Markov’s inequality.

This is a survey on recent progresses in the study of branching processes with immigration, generalized Ornstein-Uhlenbeck processes and affine Markov processes. We mainly focus on the applications of skew convolution semigroups and the connections in those processes.

In this paper, we give the Laplace transform of the first hitting times to boundary and obtain its expectation on the reflected Ornstein-Uhlenbeck process with two-sided barriers. Finally,a comparison theorem is derived. Mathematics Subject Classification: 60H10

We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller ...

We are much intersted in events with high multiplicity at RHIC, where thousands of particles are produced per event. To describe such many particle system, a sort of collective approach will be useful. One-particle rapidity or pseudo-rapidity distributions observed at RHIC are well described by the Ornstein-Uhlenbeck process with two or three sources [1]. In this paper, we would extend our appr...

For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a given starting point x and an endpoint y provided y belongs to a certain linear subspace of full measure. We derive also a stochastic evolution equation satisfied by the OU Bridge and study its basic properties. The OU Bridge is then used to investigate the Markov transition ...