Paolo Baldi

Subsampling Needlet Coefficients on the Sphere

In a recent paper, we analyzed the properties of a new kind of spherical wavelets (so-called needlets) for statistical inference procedures on spherical random fields; the results were mainly motivated by applications to cosmological data. In the present work, we exploit the asymptotic uncorrelation of random needlet coefficients at fixed angular distances to construct subsampling statistics evaluated on Voronoi cells on the sphere. We illustrate how such statistics can be used for isotropy tests and for bootstrap estimation of nuisance parameters, even when a single realization of the spherical random field is observed. The asymptotic theory is developed in details, in the high resolution sense.

Limit set of inhomogeneous Ornstein-Uhlenbeck processes, destabilization and annealing

We consider the Diffusion Process obtained by perturbing a dynamical system having a single equilibrium point x, by a fixed time-inhomogeneous Gaussian process whose intensity tends to 0 at infinity. We establish criteria for the exit time from a neighborhood of x to be a.s. finite by linking this fact with the structure of the limit set at infinity. We are also able to compute this limit set for inhomogeneous Ornstein-Uhlenbeck processes associated to linear systems. An application is given to simulated annealing.

Large and Moderate Deviations for Random Walks on Nilpotent Groups

We prove large and moderate deviation estimates for products of i.i.d. r.v.s taking values on simply connected nilpotent Lie groups as a consequence of large and moderate deviation results for stochastic processes which are solutions of O.D.E. with random coefficients.

Representation of Gaussian isotropic spin random fields

We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin line bundles of the 2-sphere. In particular, every complex Gaussian isotropic spin random field can be represented in this way. Our construction extends P. Levy’s original idea for the spherical Brownian motion.

On Lévy's Brownian motion indexed by elements of compact groups

We investigate positive definiteness of the Brownian kernel K(x,y)=1/2(d(x,x0)+d(y,x0)-d(x,y)) on a compact group G and in particular for G=SO(n).

A Diffusion Approximation Which Models Hierarchic Interactions in Cooperative Biological Systems

In this paper the diffusion approximation of a Markov chain for hierarchic cooperative interactions in proteins is considered. The behaviour of the limiting diffusion, which takes values in the closed square [0,1]2, is then studied. The existence, absolute continuity and uniqueness of the stationary distribution are proved and its ergodic and reversibility properties analyzed. The problem of the attainability of the boundary is also considered.

On Sharp Large Deviations for the Bridge of a General Diffusion

We provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a d-dimensional general diffusion process X, as the conditioning time tends to 0. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift b of X. It turns out that the sharp asymptotics for the exit probability are independent of the drift b, provided it satisfies a simple condition that is always satisfied in dimension 1. On the other hand we produce an example where this assumption is not satisfied and the drift is actually influential.