Abstract
In this paper we calculate the exact asymptotics of the probability P{‖w(t)+uct‖ p >u},u→∞, wherew(t) is the standard Wiener process and ‖x‖ p is the ordinary norm in the spaceL p[0,1],p≥2. The result is obtained on the basis of a general theorem due to the author on the asymptotics of the Gaussian measureP(uD),u→∞, for a Borel setD belonging to a separable Banach space.
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