Optimal control
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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 PA is a Gaussian measure in an infinite-dimensional Banach space B, D = {x 驴 B: Q(x) 驴 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驴驴 is a large parameter.