A Large Deviation Principle and an Expression of the Rate Function for a Discrete Stationary Gaussian Process

International audienceWe prove a Large Deviation Principle for a stationary Gaussian process over R b , indexed by Z d (for some positive integers d and b), with positive definite spectral density and provide an expression of the corresponding rate function in terms of the mean of the process and its spectral density. This result is useful in applications where such an expression is needed