Asymptotic analysis of Gaussian integrals. I. Isolated minimum points

Ellis, Richard S.; Rosen, Jay S.

doi:10.1090/S0002-9947-1982-0667156-0

Asymptotic analysis of Gaussian integrals. I. Isolated minimum points

Authors: Richard S. Ellis and Jay S. Rosen
Journal: Trans. Amer. Math. Soc. 273 (1982), 447-481
MSC: Primary 60G15; Secondary 28C20, 58D20, 81C35
DOI: https://doi.org/10.1090/S0002-9947-1982-0667156-0
MathSciNet review: 667156
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Abstract: This paper derives the asymptotic expansions of a wide class of Gaussian function space integrals under the assumption that the minimum points of the action are isolated. Degenerate as well as nondegenerate minimum points are allowed. This paper also derives limit theorems for related probability measures which correspond roughly to the law of large numbers and the central limit theorem. In the degenerate case, the limits are non-Gaussian.

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