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A Cameron-Martin type formula for general Gaussian processes: A filtering approach. (English) Zbl 1002.60031
A Cameron-Martin type formula is derived for the Laplace transform of some integrals of the square of a general continuous Gaussian process. The formula involves in particular the variance of the filtering error in some auxiliary optimal filtering problem which is used in the proof. This variance is expressed in terms of the solution of a Riccati-Volterra type integral equation containing the covariance function of the process. In various specific cases this equation is solved and then the formula becomes completely explicit.

MSC:
60G15 Gaussian processes
60G44 Martingales with continuous parameter
62M20 Inference from stochastic processes and prediction
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