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Currently displaying 1 – 2 of 2

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Grandes déviations et loi fonctionnelle du logarithme itéré pour les processus de diffusions avec réflexion

Toussaint Joseph Rabeherimanana — 2007

Annales mathématiques Blaise Pascal

Dans cet article, nous démontrons une loi fonctionnelle du logarithme itéré pour les diffusions avec réflexion à la frontière d’un ouvert régulier $D_{0}$ de $ℝ^{n}$ semblable à la loi de Strassen [] pour le brownien et de Baldi [] pour les diffusions en utilisant la technique de grandes déviations.

Nouveaux résultats sur les petites perturbations d’équations d’évolutions aléatoires

Lyliane Irène Rajaonarison; Toussaint Joseph Rabeherimanana — 2012

Annales mathématiques Blaise Pascal

Dans cet article, nous étudions les résultats de grandes déviations associés au couple $(X^{ε}, ν^{ε})$ , solution de l’E.D.S. interprétée au sens d’Itô : $d X_{t}^{ε} = \sqrt{ε} σ_{ν^{ε} (t)} (X_{t}^{ε}) d W_{t} + b_{ν^{ε} (t)} (X_{t}^{ε}) d t; X_{0}^{ε} = x \in ℝ^{d}$ avec des conditions assez générales sur les coefficients et dans les deux cas suivants : Premier cas : $ν^{ε}$ est indépendant du mouvement brownien $W$ et satisfait à un principe de grandes déviations ; Deuxième cas : $ν^{ε}$ est un processus...

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