Higher asymptotics of Laplace's approximation
| Autor: | William D. Kirwin |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Asymptotic analysis
Smoothness (probability theory) Laplace transform Explicit formulae General Mathematics Multiple integral Mathematical analysis FOS: Physical sciences Mathematical Physics (math-ph) Type (model theory) Term (logic) Mathematics - Classical Analysis and ODEs 41A60 41A63 44A10 Classical Analysis and ODEs (math.CA) FOS: Mathematics Asymptotic expansion Mathematical Physics Mathematics |
| Zdroj: | Asymptotic Analysis. 70:231-248 |
| ISSN: | 0921-7134 |
| DOI: | 10.3233/asy-2010-1016 |
| Popis: | We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the integrand. Our most general result assumes no smoothness of the functions of the integrand, but the expressions we obtain contain integrals which may be difficult to evaluate in practice. We then make additional assumptions which are sufficient to simplify these integrals, in some cases obtaining explicit formulae for the coefficients in the asymptotic expansions. Comment: 8 pages; v2 significant expansion, several corollaries of main theorem added, minor corrections |
| Databáze: | OpenAIRE |
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