TY - JOUR
T1 - Asymptotics of Gaussian Integrals in Infinite Dimensions
AU - Steblovskaya, Victoria
AU - Albeverio, Sergio
N1 - Publisher Copyright:
© 2019 World Scientific Publishing Company.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
M3 - Article
VL - Vol. 22
SP - 28 pages
JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics
JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics
IS - No. 1 (2019) 1950004
ER -