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...

The hole probability that the zero set of the time dependent planar Gaussian analytic function fC(z, t) = ∞ ∑ n=0 an(t) zn √ n! , (1) where an(t) are i.i.d. complex valued Ornstein-Uhlenbeck processes, does not intersect a disk of radius R for all t ∈ [0, T ] decays like exp(−TecR2). This result sharply differentiates the zero set of fC from a number of canonical evolving planar point processes...

We consider the Kuramoto model of globally coupled phase oscillators subject to Ornstein-Uhlenbeck and non-Gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process. We use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise, and...

Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order structure of the volatility, the log returns, as well as their “squares” are discussed in detail. M...

Jaume Masoliver‡ Departament de F́ısica Fonamental, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Spain (Dated: May 28, 2008) Abstract We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a ...