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P-th Mean Almost Periodic Random Functions

  • Paul H. Bezandry
  • Toka Diagana
Chapter

Abstract

Chapter 4 introduces the concept of p-th mean almost periodicity is introduced. It is shown that each p-th mean almost periodic stochastic process defined on a probability space (\(\Omega, \mathcal{F}, \mathbf{P}\)) is uniformly continuous and stochastically bounded. The collection of such stochastic processes is a Banach space when it is equipped with its natural norm. Moreover, two composition theorems for p-th mean almost periodic processes (Theorem 4.4 and Theorem 4.5) are established. They play a crucial role in the study of the existence (and uniqueness) of p-th mean almost periodic solutions to various stochastic differential equations on \(L^{P} (\Omega, \mathbb{H})\) where \(\mathbb{H}\) is a real separable Hilbert space.

Keywords

Banach Space Stochastic Process Periodic Solution Periodic Function Stochastic Differential Equation 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsHoward UniversityWashingtonUSA

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