Large deviations of theL p-norm of a wiener process with drift

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 ^p0,1],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. Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 429–436, March, 1999.