A Gaussian process is a stochastic process Xt, t ∈ T, for which any finite linear combination of samples has a joint Gaussian distribution. More accurately, any linear functional applied to the sample function Xt will give a normally distributed result. Notation-wise, one can write X ∼ GP(m, K), meaning: the random function X "is distributed as a GP with mean function m and covariance function K". When the input vector t is two- or multi-dimensional a Gaussian process might be also known as a Gaussian random field.
Some authors assume the random variables Xt have mean zero; this greatly simplifies calculations without loss of generality and allows the mean square properties of the process to be entirely determined by the covariance function K.
Read more about Gaussian Process: Alternative Definitions, Covariance Functions, Important Gaussian Processes, Applications
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