Gaussian Process - Alternative Definitions

Alternative Definitions

Alternatively, a process is Gaussian if and only if for every finite set of indices in the index set

is a multivariate Gaussian random variable. Using characteristic functions of random variables, the Gaussian property can be formulated as follows: is Gaussian if and only if, for every finite set of indices, there are reals with and reals such that

The numbers and can be shown to be the covariances and means of the variables in the process.

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