Asymptotically periodic solution of a stochastic differential equation

Solution asymptotiquement périodique d'une classe d'équation différentielle stochastique

Solym Manou-Abi (1, 2) , William Dimbour (3)

1 CUFR - Centre Universitaire de Formation et de Recherche de Mayotte
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 ESPACE-DEV - Département Environnement et Ressources [Montpellier]

In this paper, we first introduce the concept and properties of ω-periodic limit process. Then we apply specific criteria obtained to investigate asymptotically ω-periodic mild solutions of a Stochastic Differential Equation driven by a Brownian motion. Finally, we give an example to show usefulness of the theoritical results that we obtain in the paper. MSC : 34C25, 34C27, 60H30, 34 F05.

Mots clés: Semigroup Mild solution; Square-mean asymptotically periodic; Stochastic differential equation; Square-mean periodic limit

Domaines: Systèmes dynamiques [math.DS]; Statistiques [math.ST]

Solym Manou-Abi, William Dimbour. Asymptotically periodic solution of a stochastic differential equation. Bulletin of the Malaysian Mathematical Sciences Society, inPress, pp.1-29. ⟨10.1007/s40840-019-00717-9⟩. ⟨hal-02063734⟩