Sur une question de probabilité
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
We study points of density of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.
We consider a homogeneous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the decay of the largest fragment for parameter values that allow for survival. In this respect the present paper is also concerned with the probability of extinction of the killed process.
Given an autoregressive process X of order p (i.e. Xn = a1Xn−1 + ··· + apXn−p + Yn where the random variables Y1, Y2,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time N (survival or persistence probability). Depending on the coefficients a1,..., ap and the distribution of Y1, we state conditions under which the survival probability decays polynomially, faster than polynomially or converges to a positive constant....
The main objective of this paper is to present a new probabilistic model underlying the universal relaxation laws observed in many fields of science where we associate the survival probability of the system's state with the defect-diffusion framework. Our approach is based on the notion of the continuous-time random walk. To derive the properties of the survival probability of a system we explore the limit theorems concerning either the summation or the extremes: maxima and minima. The forms of...
We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.
A model of a heterogeneous population partitioned into a finite number of classes according an exchangeable equivalence relation is studied. With this motivation the properties of exchangeable equivalence relations are investigated and, in particular, the structure of its equivalence classes is characterized.