Almost sure uniform convergence of a random Gaussian field conditioned on a large linear form to a non random profile

Publication date: Available online 21 January 2019Source: Statistics & Probability LettersAuthor(s): Philippe MounaixAbstractWe investigate the realizations of a random Gaussian field on a finite domain of Rd in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and almost surely to a non random profile depending only on the covariance and the considered linear functional of the field. This is a significant improvement of the weaker L2-convergence in probability previously obtained in the case of conditioning on a large quadratic functional.

Source: Statistics and Probability Letters - January 21, 2019 Category: Statistics Source Type: research