Level sets of random fields and applications: specular points and wave crests.
40 years of probability in Venezuela.
Central limit theorem for solutions of random initialized differential equations: a simple proof.
Asymptotic behaviour of the quadratic measure of deviation of multivariate density estimates
Asymptotics for the -deviation of the variance estimator under diffusion
We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate with window of a function of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the deviations such as
Asymptotics for the -deviation of the variance estimator under diffusion
We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate with window of a function of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the deviations such as
Estimation in models driven by fractional brownian motion
Let { (), ∈ℝ} be the fractional brownian motion with parameter 0<<1. When 1/2<, we consider diffusion equations of the type ()=+ (()) d ()+ (()) d. In different particular models where ()= or ()= and ()= or ()= , we propose a central limit theorem for estimators of and of based on regression methods. Then we give tests...
On the central limit theorem in Hilbert space.
The object of this paper is to prove a central limit theorem in (separable) Hilbert space using a method based on the so called découpage de Lévy, the Lindeberg proof for the Gaussian case and an elementary proof of Poisson convergence for the direct part, and on elementary probabilistic inequalities for the converse. In particular, characteristic functions are only used in unicity questions. Several results of Varadhan (1962) can be obtained either directly as corollaries of the main theorem or...
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