The paper presents a cointegration model in continuous time, where the linear combinations of the integrated processes are modeled by a multivariate Ornstein-Uhlenbeck process. The integrated processes are defined as vector-valued Lévy processes with an additional noise term. Hence, if we observe the process at discrete time points, we obtain a multiple regression model. As an estimator for the...

In this article, we propose several quantization based stratified sampling methods to reduce the variance of a Monte-Carlo simulation. Theoretical aspects of stratification lead to a strong link between the problem of optimal Lquantization of a random variable and the variance reduction that can be achieved. We first emphasize on the consistency of quantization for designing strata in stratifie...

Customers arrive at rate N α on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate β. We let N go to infinity. We prove a functional central limit theorem (CLT) for the tails of the empirical measures of the queue occupations, in a Hilbert space with the weak topology, with limit given by an Ornstein-Uhlenb...

The solution of the Ornstein-Zernike equation with various closure approximations is studied. This problem is rewritten as an integral equation that can be solved iteratively on a grid. The convergence of the xed point iterations is relatively slow. We consider transformations of the sequence of solution vectors using non-linear sequence transformations, so-called vector extrapolation processes...

Multiple scattering becomes a problem close to the critical point, especially in systems with a large difference in the refractive index and large correlation length amplitudes as for the case of polystyrene/cyclohexane. In this work we demonstrate the application of the one-beam cross correlation technique and show that in the reduced temperature range of t red51.66310 25 – 0.03 the multiple s...

Customers arrive at rate Nα on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate β. We let N go to infinity. We prove a functional central limit theorem (CLT) for the tails of the empirical measures of the queue occupations, in a Hilbert space with the weak topology, with limit given by an Ornstein-Uhlenbe...

Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression. In this paper we propose a characteristic function-based estimation method for non-Gaussian Ornstein-Uhl...

For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a starting point x and an endpoint y that 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 semigroup as...

This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/∞ queue. They describe in particular the exponential dissipation of Φ-entropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the O...

We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularisation in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE). Our aim is the estimation of the SDE parameters. We use the main advantage of a one-dimensional observation to obtain an easy way to compute the exact likelihood using the Kalm...