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 ...

Let G be an almost simple simply-connected algebraic group over C with the Lie algebra g. Let h be a Cartan subalgebra of g. We assume G is of type ADE, as there arise technical issues for type BCFG. (We will remark them at relevant places. See footnotes 5, 12.) At some points, particularly in this introduction, we want to include the case G = GL(r). We will not make clear distinction between t...

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...

The discrete Uehling-Uhlenbeck equations are solved to study the propagation of plane (sound) waves in a system of composite fermionic particles with hard-sphere interactions and the filling factor (ν) being 1/2. The Uehling-Uhlenbeck collision sum, as it is highly nonlinear, is linearized firstly and then decomposed by using the plane wave assumption. We compare the dispersion relations thus o...

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 ...

Starting with the work of Yau [Y1], Donaldson [D1], and Uhlenbeck-Yau [UY], the notion of stability has revealed itself under many guises to be closely related to the existence of canonical metrics in Kähler geometry. The equivalence between Hermitian-Einstein metrics on vector bundles and Mumford stability was proved by Donaldson and Uhlenbeck-Yau in [D1] and [UY], while the existence of Kähle...

This paper considers the problem of a capital-limited investor with log utility who has the opportunity to invest in a security that follows a parametric price process. While the investor knows the form of the process, the exact parameter values are not known and must be inferred by observing the evolution of the security's price over time. The approach that will be described is applicable to a...