Exact asymptotics of Laplace-type Wiener integrals for Lp-functionals

We prove theorems on the exact asymptotic behaviour of the integrals E exp{u(integral(1)(0)|xi(t)|(p) dt)(alpha/p)}, E exp{-u integral(1)(0)|xi(t)|(p) dt}, u --> infinity, for p > 0 and 0 < alpha < 2 for two random processes xi(t), namely, the Wiener process and the Brownian bridge, and obtain other related results. Our approach is via the Laplace method for infinite-dimensional distributions, namely, Gaussian measures and the occupation time for Markov processes.