Orthogonal Expansions

Part of the Springer Monographs in Mathematics book series (SMM)


While most of what we shall have to say in this brief chapter is rather theoretical, it actually covers one of the most important practical aspects of Gaussian modeling. The basic result is Theorem 3.1.1, which states that every centered Gaussian process with a continuous covariance function has an expansion of the form where the ξn are i.i.d. N(0, 1), and the ϕn are certain functions on T determined by the covariance function C of f . In general, the convergence in (3.0.1) is in L2({ℙ) for each tT , but (Theorem 3.1.2) if f is a.s. continuous then the convergence is uniform over T , with probability one.


Orthonormal Basis Covariance Function Reproduce Kernel Hilbert Space Standard Brownian Motion Orthogonal Expansion 
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© Springer Science+Business Media LLC 2007

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