Statistical Models and Turbulence pp 27-40 | Cite as

# Probability limit theorems and some questions in fluid mechanics 1)

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## Abstract

A number of problems in fluid mechanics which have been dealt with by making use of a central limit theorem (and asymptotic normality) are mentioned. A discussion of central limit theorems for stationary processes and the need for some form of asymptotic independence is given.The concepts of uniform ergodicity and strong mixing are introduced.An example of asymptotic nonnormality is given when the form of asymptotic independence is not sufficiently strong.The derivation of a new result indicating that uniform ergodicity is strong mixing when there is trivial tail field is briefly sketched.

## Keywords

Central Limit Theorem Asymptotic Normality Stationary Sequence Folk Theorem Asymptotic Independence
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## Copyright information

© Springer-Verlag 1972