Asymptotics of Gaussian integrals in infinite dimensions-Reference-Cited by-同舟云学术

Asymptotics of Gaussian integrals in infinite dimensions

Published:2019-03 Issue:01 Volume:22 Page:1950004
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

Albeverio Sergio¹,Steblovskaya Victoria²

Affiliation:

1. Institut fuer Angewandte Mathematik, Universitaet Bonn, Endenicher Allee 60, D-53115 Bonn, HCM; SFB 611; BiBoS; CERFIM (Locarno), Germany

2. Department of Mathematical Sciences, Bentley University, 175 Forest Street, Waltham, MA 02452 4705, USA

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025719500048

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