ABSTRACT
This chapter provides a brief introduction to some elementary concepts in Gaussian processes. Since regular variation has a major role in the statements and proofs of the main results, it presents a short survey of the basic theory of J. Karamata. The most widely studied Gaussian process is the standard Brownian motion process, known as the Wiener process. A more general form of G is obtained when the hypothesis of station-arity is weakened to a form of “local stationarity.” The first such result was for the case of a Gaussian process with stationary increments by Simeon M. Berman. If the mean function of a Gaussian process is constant and its covariance function satisfies, then the process is stationary.
