Gaussian Process

A Gaussian process is a stochastic process X_t, 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 X_t 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 X_t 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.