When the noise is white gaussian process, , the signal power.

Many popular interpolation tools are actually equivalent to particular Gaussian processes.

Gaussian processes are important in statistical modelling because of properties inherited from the normal.

A key fact of Gaussian processes is that they can be completely defined by their second-order statistics.

It is actually equivalent to a Gaussian process model with covariance function:

An important example of an ergodic processes is the stationary Gaussian process with continuous spectrum.

Sample paths of a Gaussian process with the exponential covariance function are not smooth.

In the geostatistics community Gaussian process regression is also known as Kriging.

The Brownian bridge is a Gaussian process whose increments are not independent.

In general, a Gaussian process is time-reversible.

In particular, follows a Gaussian process.

Thus, if a Gaussian process is assumed to have mean zero, defining the covariance function completely defines the process' behaviour.

The Wiener process is perhaps the most widely studied Gaussian process.

Recently, "treed" Gaussian processes have been used to deal with heteroscedastic and discontinuous responses.

This method uses Gaussian process regression to fit a probabilistic model from which replicates may then be drawn.

Gaussian process is a powerful non-linear interpolation tool.

The Gaussian process emulator model treats the problem from the viewpoint of Bayesian statistics.

As such, Gaussian processes are useful as a powerful non-linear interpolation tool.

Note that the experimental variogram is an empirical estimate of the covariance of a Gaussian process.

A Gaussian process with Matérn covariance has sample paths that are times differentiable.

Fractional Brownian motion is the only self-similar Gaussian process.

A Gaussian process can be used as a prior probability distribution over functions in Bayesian inference.

Gaussian processes are the normally distributed stochastic processes.

Ray-Knight type theorems relate the field L to an associated Gaussian process.

For example, if a random process is modelled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly.