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. Problems of Information Transmission Springer Journals

The Laplace method for Gaussian measures and integrals in Banach spaces

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Springer US
Copyright © 2013 by Pleiades Publishing, Inc.
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
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