Mauro Piccioni

The empirical process on Gaussian spherical harmonics

We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literature, in connection with the statistical analysis of cosmic microwave background radiation.

A representation formula for the large deviation rate function for the empirical law of a continuous time Markov chain

We prove a representation formula for the rate function of the Large Deviation Principle for the empirical distribution of an irreducible continuous time Markov process on a finite state space. We use this representation to characterize asymptotically efficient intensities for the Monte Carlo evaluation of probabilities of a large deviation for the empirical distribution.

Dirichlet random walks

This paper provides tools for the study of the Dirichlet random walk in R d . We compute explicitly, for a number of cases, the distribution of the random variable W using a form of Stieltjes transform of W instead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caer (2010), (2011). We extend our results to the study of the limits of the Dirichlet random walk when the number of added terms goes to ∞, interpreting the results in terms of an integral by a Dirichlet process. We introduce the ideas of Dirichlet semigroups and Dirichlet infinite divisibility and characterize these infinite divisible distributions in the sense of Dirichlet when they are concentrated on the unit sphere of R d .

Linear smoothing as an optimal control problem

Abstract A characterization of the optimal smoother for a linear stochastic system is given as the optimal trajectory of a related control problem. As a corollary a more direct proof of a known stochastic representation for the minimizer of some regularizing functionals is obtained.

Perfect Simulation of Autoregressive Models with Infinite Memory

In this paper we consider the problem of determining the law of binary stochastic processes from transition kernels depending on the whole past. These kernels are linear in the past values of the process. They are allowed to assume values close to both 0 and 1, preventing the application of usual results on uniqueness. We give sufficient conditions for uniqueness and non-uniqueness; in the former case a perfect simulation algorithm is also given.

One-Dimensional Infinite Memory Imitation Models with Noise

In this paper we study stochastic process indexed by

Dirichlet curves, convex order and Cauchy distribution

\mathbb {Z}

Functionally Compatible Local Characteristics for the Local Specification of Priors in Graphical Models

Z constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a previous random instant. We characterize uniqueness in terms of simple concepts concerning families of stochastic matrices, generalizing the results previously obtained in De Santis and Piccioni (J Stat Phys 150(6):1017–1029, 2013).