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- Title
Measure Theory and Square-Mean Pseudo Almost Periodic and Automorphic Process: Application to Stochastic Evolution Equations.
- Authors
Diop, Mamadou Abdoul; Ezzinbi, Khalil; Mbaye, Mamadou Moustapha
- Abstract
In this work, we establish a new concept of square-mean pseudo almost periodic and automorphic processes using the measure theory. We use the $${\mu }\!-$$ ergodic process to define the spaces of $${\mu }\!-$$ pseudo almost periodic and automorphic processes in the square-mean sense. We establish many interesting results on those spaces like completeness and composition theorems. Then, we study the existence, the uniqueness, and the stability of the square-mean $${\mu }\!-$$ pseudo almost periodic and automorphic solutions of the stochastic evolution equation. We provide an example to illustrate ours results.
- Subjects
MEASURE theory; AUTOMORPHIC forms; STOCHASTIC processes; EVOLUTION equations; COMPLETENESS theorem
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2018, Vol 41, Issue 1, p287
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-015-0278-y