Volume 10 Issue 2
A Large Deviation Principle and an Expression of the Rate Function for a Discrete Stationary Gaussian Process
Olivier Faugeras and James MacLaurin
INRIA Sophia Antipolis Mediterannee, 2004 Route Des Lucioles, Sophia Antipolis, France
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Abstract
We prove a large deviation principle for a stationary Gaussian process over ℝb indexed by ℤd (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.
Keywords:stationary Gaussian process; large deviation principle; spectral density