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On the asymptotic Laplace method and its application to random chaos. (English. Russian original) Zbl 1326.60045

Math. Notes 97, No. 6, 878-891 (2015); translation from Mat. Zametki 97, No. 6, 868-883 (2015).
Summary: The asymptotics of the multidimensional Laplace integral for the case in which the phase attains its minimum on an arbitrary smooth manifold is studied. Applications to the study of the asymptotics of the distribution of Gaussian and Weibullian random chaoses are considered.

MSC:

60G15 Gaussian processes
44A10 Laplace transform
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