Existence and global attractiveness of a square‐mean μ‐pseudo almost automorphic solution for some stochastic evolution equation driven by Lévy noise. Issue 8 (22nd September 2016)

• Record Type: Journal Article
• Authors: Diop, Mamadou Abdoul; Ezzinbi, Khalil; Mbaye, Mamadou Moustapha
• Is Part Of: Mathematische Nachrichten. Volume 290:Issue 8/9(2017)
• Page Start: 1260
• Page End: 1280
• Publication Date: 2016-09-22
• Subjects: Measure theory -- ergodicity -- μ‐pseudo almost automorphic solution -- composition theorem -- stochastic processes -- stochastic evolution equations -- Lévy noise -- 34C27 -- 34K14 -- 34K30 -- 34K50 -- 35B15 -- 35K55 -- 43A60 -- 60G20; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201500345
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : In this work, we introduce the concept of μ‐pseudo almost automorphic processes in distribution. We use the μ‐ergodic process to define the spaces of μ‐pseudo almost automorphic processes in the square mean sense. We establish many interesting results on the functional space of such processes like a composition theorem. Under some appropriate assumptions, we establish the existence, the uniqueness and the stability of the square‐mean μ‐pseudo almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Lévy noise. We provide an example to illustrate our results.