EXISTENCE OF ALMOST AUTOMORPHIC SOLUTION IN DISTRIBUTION FOR A CLASS OF STOCHASTIC INTEGRO-DIFFERENTIAL EQUATION DRIVEN BY LÉVY NOISE

Mamadou Moustapha Mbaye , Solym Manou-Abi (1, 2)

1 CUFR - Centre Universitaire de Formation et de Recherche de Mayotte
2 IMAG - Institut Montpelliérain Alexander Grothendieck

We investigate a class of stochastic integro-differential equations driven by Lévy noise. Under some appropriate assumptions, we establish the existence of an square-mean almost automorphic solutions in distribution. Particularly, based on Schauder's fixed point theorem, the existence of square-mean almost automorphic mild solution distribution is obtained by using the condition which is weaker than Lipschitz conditions. We provide an example to illustrate ours results.

Domaines: Mathématiques [math]

Mamadou Moustapha Mbaye, Solym Manou-Abi. EXISTENCE OF ALMOST AUTOMORPHIC SOLUTION IN DISTRIBUTION FOR A CLASS OF STOCHASTIC INTEGRO-DIFFERENTIAL EQUATION DRIVEN BY LÉVY NOISE. 2020. ⟨hal-02974673⟩