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The Gaussian Process

Module by: Don Johnson. E-mail the author

A random process X⁢t X t is Gaussian if the joint density of the NN amplitudes X⁢ t 1 …,X⁢ t N X t 1 …, X t N comprise a Gaussian random vector. The elements of the required covariance matrix equal the covariance between the appropriate amplitudes: Ki,j= K X ⁢ t i t j K i j K X t i t j . Assuming the mean is known, the entire structure of the Gaussian random process is specified once the correlation function or, equivalently, the power spectrum is known. As linear transformations of Gaussian random processes yield another Gaussian process, linear operations such as differentiation, integration, linear filtering, sampling, and summation with other Gaussian processes result in a Gaussian process.

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