The Gaussian Process 1.2 2003/05/16 2003/08/04 17:18:04.228 GMT-5 Don Johnson dhj@rice.edu Don Johnson dhj@rice.edu Eileen Krause erkrause@rice.edu Kyle Clarkson kclarks@rice.edu Elizabeth Gregory lizzardg@rice.edu Kevin Duh kevinduh@rice.edu Mariyah Poonawala mariyah@rice.edu Matthew Jeanes mjeanes@rice.edu Jeffrey Silverman jsilv@rice.edu A random process X t is Gaussian if the joint density of the N amplitudes 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: 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.