Date/heure
15 décembre 2022
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Anna Melnykova (Université d'Avignon)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
We develop a statistical test on the determinant of the diffusion coefficient in a 1 or 2-dimensional stochastic differential equations from discrete observations on a fixed time interval [0,T] sampled with a fixed time step.
We propose a test statistic based on increments of the process which guarantees the control of the level of the test in a non asymptotic setting. In dimension 1, the test density is known explicitly even when the drift is estimated. We construct the test and give conditions under which the Type I and Type II errors can be controlled. In dimension 2, the test statistic has not an explicit density but upper and lower bounds are provided. We then give conditions under which the Type I and Type II errors of the test procedure can be controlled. A numerical study illustrates the properties of the tests for stochastic processes with known or unknown drifts.