Percolation transition for some excursion sets.
Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
For stationary Gaussian processes, we obtain the necessary and sufficient conditions for Poincaré inequality and log-Sobolev inequality of process-level and provide the sharp constants. The extension to moving average processes is also presented, as well as several concrete examples.
Poisson kernel and Green function of balls for complex hyperbolic Brownian motion
The aim of this paper is to give a description of the Poisson kernel and the Green function of balls in the complex hyperbolic space. The description is in terms of the hypergeometric function and unitary spherical harmonics in ℂⁿ.
Power variation of multiple fractional integrals
Precise small deviations in L 2 of some Gaussian processes appearing in the regression context
We find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.
Probabilistic and analytic formulas for the periodic splines interpolating with multiple nodes
Processus gaussiens à variation finie
Processus gaussiens, markoviens d'ordre p, fortement markoviens d'ordre p et problème de Dirichlet stochastique
Product -actions on a Lebesgue space and their applications
We define a class of -actions, d ≥ 2, called product -actions. For every such action we find a connection between its spectrum and the spectra of automorphisms generating this action. We prove that for any subset A of the positive integers such that 1 ∈ A there exists a weakly mixing -action, d≥2, having A as the set of essential values of its multiplicity function. We also apply this class to construct an ergodic -action with Lebesgue component of multiplicity , where k is an arbitrary positive...
Propriétés markoviennes de processus sur R2