P-th Mean Almost Periodic Random Functions

Paul H. Bezandry () and Toka Diagana ()
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Paul H. Bezandry: Howard University, Department of Mathematics
Toka Diagana: Howard University, Department of Mathematics

Chapter Chapter 4 in Almost Periodic Stochastic Processes, 2011, pp 117-127 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-9476-9_4

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DOI: 10.1007/978-1-4419-9476-9_4

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