Exact Asymptotics of Laplace Integrals for Nonsmooth Functions
Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 886-890
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In this paper, we calculate the exact asymptotics with remainder of integrals of Laplace type in an arbitrary space, without imposing any constraints on the smoothness of the functions. As a special case, we derive the classical Laplace formula. Some examples are given.
@article{MZM_2003_73_6_a9,
author = {E. I. Ostrovskii},
title = {Exact {Asymptotics} of {Laplace} {Integrals} for {Nonsmooth} {Functions}},
journal = {Matemati\v{c}eskie zametki},
pages = {886--890},
year = {2003},
volume = {73},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a9/}
}
E. I. Ostrovskii. Exact Asymptotics of Laplace Integrals for Nonsmooth Functions. Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 886-890. http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a9/
[1] Maslov V. P., Fedoryuk M. V., “Logarifmicheskaya asimptotika integralov Laplasa”, Matem. zametki, 30 (1981), 880–883
[2] Fedoryuk M. V., Asimptotika. Integraly i ryady, Nauka, M., 1987
[3] Piterbarg V. I., Asimptoticheskie metody v teorii gaussovskikh sluchainykh protsessov i polei, MGU, M., 1984
[4] Ostrovskii E. I., “Tochnaya asimptotika plotnosti raspredeleniya kratnykh stokhasticheskikh integralov”, Problemy peredachi informatsii, 28:3 (1992), 60–67 | MR | Zbl
[5] Ostrovskii E. I., Eksponentsialnye otsenki dlya sluchainykh polei i ikh primeneniya, OIATE, Obninsk, 1999
[6] Attiyah M. F., “Resolution of singularities and division of distributions”, Comm. Pure Appl. Math., 23:2 (1970), 145–150 | DOI | MR