# The Laplace method for Gaussian measures and integrals in Banach spaces

The Laplace method for Gaussian measures and integrals in Banach spaces We prove results on tight asymptotics of probabilities and integrals of the form $P_A (uD)andJ_u (D) = \int\limits_D {f(x)\exp \{ - u^2 F(x)\} dP_A (ux)}$ , where P A is a Gaussian measure in an infinite-dimensional Banach space B, D = {x ∈ B: Q(x) ≥ 0} is a Borel set in B, Q and F are continuous functions which are smooth in neighborhoods of minimum points of the rate function, f is a continuous real-valued function, and u→∞ is a large parameter. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# The Laplace method for Gaussian measures and integrals in Banach spaces

, Volume 49 (4) – Jan 25, 2014
21 pages

/lp/springer_journal/the-laplace-method-for-gaussian-measures-and-integrals-in-banach-n6aU2GXeLl
Publisher
Springer Journals
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946013040066
Publisher site
See Article on Publisher Site

### Abstract

We prove results on tight asymptotics of probabilities and integrals of the form $P_A (uD)andJ_u (D) = \int\limits_D {f(x)\exp \{ - u^2 F(x)\} dP_A (ux)}$ , where P A is a Gaussian measure in an infinite-dimensional Banach space B, D = {x ∈ B: Q(x) ≥ 0} is a Borel set in B, Q and F are continuous functions which are smooth in neighborhoods of minimum points of the rate function, f is a continuous real-valued function, and u→∞ is a large parameter.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Jan 25, 2014

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