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Asymptotics for the L p -deviation of the variance estimator under diffusion

Paul DoukhanJosé R. León — 2004

ESAIM: Probability and Statistics

We consider a diffusion process X t smoothed with (small) sampling parameter ε . As in Berzin, León and Ortega (2001), we consider a kernel estimate α ^ ε with window h ( ε ) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the L p deviations such as 1 h h ε p 2 α ^ ε - α p p - 𝔼 α ^ ε - α p p .

Asymptotics for the -deviation of the variance estimator under diffusion

Paul DoukhanJosé R. León — 2010

ESAIM: Probability and Statistics

We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate α ^ ε 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 1 h h ε p 2 α ^ ε - α p p - I E α ^ ε - α p p .

Estimation in models driven by fractional brownian motion

Corinne BerzinJosé R. León — 2008

Annales de l'I.H.P. Probabilités et statistiques

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.

Evarist GinéJosé R. León — 1980

Stochastica

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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