Estimates for the distribution of the supremum of square-Gaussian stochastic processes defined on noncompact sets

Estimates for the distribution of the supremum of square-Gaussian stochastic processes defined on R+ are found in the paper. Using these results, we find estimates for the deviation in the uniform metric between the correlogram and the correlation function of a real stationary Gaussian stochastic process. A criterion for testing a hypothesis concerning the correlation function is also constructed.