MEAN (µ, ν)-PSEUDO ALMOST PERIODIC SOLUTIONS OF CLASS r UNDER THE ANGLE OF MEASURE THEORY TO SOME STOCHASTIC EVOLUTION EQUATIONS

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Résumé

The paper introduces and studies the concept of mean
(µ, ν)-pseudo almost periodic solution of class r for stochastic processes
using the measure theory. We use (µ, ν)-ergodic process to define the spaces
of (µ, ν)-pseudo almost periodic processes of class r in the mean sense. We
also present many interesting results on this spaces, such as completeness
and composition theorems. Our abstract results are subsequently applied
to investigate the existence and uniqueness of mean almost pseudo periodic
solutions for the stochastic evolution equation.

Mots-clés

Poisson process, Markov process, C0-semigroup, (µ, ν)-ergodic process, (µ, ν)-pseudo almost periodic process, stochastic processes, stochastic evolution equations, Banach space.