The linear Ornstein-Ulenbeck diffusion model is too simple to describe the movement of short term interest rates. However diffusions with a non-linear drift and volatility function have no closed form likelihood function which make inference either classical or Bayesian very problematic. A vast range of approximation were proposed in the literature. In this paper, we develop the idea of a non-l...

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 ...

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...

Ornstein-Uhlenbeck models are continuous-time processes which have broad applications in finance as, e.g., volatility processes in stochastic volatility models or spread models in spread options and pairs trading. The paper presents a least squares estimator for the model parameter in a multivariate Ornstein-Uhlenbeck model driven by a multivariate regularly varying Lévy process with infinite v...

We analyze in this work the effect of the iterated application of the linear operator that maps a Wiener process onto an OrnsteinUhlenbeck process. The processes obtained after p iterations are called Ornstein-Uhlenbeck processes of order p (denoted OU(p)). Technically our composition of operators is easy to manipulate and its parameters can be computed efficiently because, as we show, in most ...

A new numerical technique for solving the Ornstein-Zernike equation is described. It is particularly useful in solving the Ornstein Zernike equation for approximations and pair potentials (such as the Percus-Yevick and mean spherical approximations for finite ranged potentials) which imply a finiteranged direct correlation function since for such approximations the numerical technique is essent...