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Erschienen in:
2011 | OriginalPaper | Buchkapitel
P-th Mean Almost Periodic Random Functions
verfasst von : Paul H. Bezandry, Toka Diagana
Erschienen in: Almost Periodic Stochastic Processes
Verlag: Springer New York
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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.