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Volume 8, Number 5, 2018, Pages 1396-1440                                                                DOI:10.11948/2018.1396
Pseudo almost periodic in distribution solutions and optimal solutions to impulsive partial stochastic differential equations with infinite delay
Zuomao Yan,Xiumei Jia
Keywords:Impulsive partial stochastic differential equations, pseudo almost periodic in distribution solutions, optimal solutions, infinite delay, fixed point.
Abstract:
      In this paper, we study a general class of impulsive partial stochastic differential equations with infinite delay and pseudo almost periodic coefficients in Hilbert spaces. Firstly, a more appropriate concept of pseudo almost periodic in distribution for stochastic processes of infinite class is introduced. Secondly, the existence of pseudo almost periodic in distribution mild solutions is investigated by utilizing the interpolation theory, the stochastic analysis techniques and fixed point theorem. The existence of optimal mild solutions of the systems is also proved. Finally, an example is provided to show the effectiveness of the theoretical results.
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