Asymptotics of Gaussian integrals in infinite dimensions

被引：3

作者：

Albeverio, Sergio ^{[1
,2
,3
,4
]}

Steblovskaya, Victoria ^{[5
]}

机构：

[1] Univ Bonn, Inst Angew Math, Endenicher Allee 60, D-53115 Bonn, Germany

[2] CERFIM, HCM, Locarno, Switzerland

[3] CERFIM, SFB 611, Locarno, Switzerland

[4] CERFIM, BiBoS, Locarno, Switzerland

[5] Bentley Univ, Dept Math Sci, 175 Forest St, Waltham, MA 02452 USA

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2019年 / 22卷 / 01期

关键词：

Asymptotic expansions; Gaussian integrals on Hilbert spaces; Laplace method; degenerate phase function; OSCILLATORY INTEGRALS; STATIONARY-PHASE; LIMIT; SPACE;

D O I：

10.1142/S0219025719500048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce an infinite-dimensional version of the classical Laplace method, in its original form, relative to a canonical Gaussian measure associated with a Hilbert space, and for a general phase function. Particular attention is given to the case of a phase function with finite-dimensional degeneracy. Explicit results on expansions in the form of power series in the relevant parameter, with estimates on remainders, are provided.

引用

页数：28

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