Negative-order moments for Lp-functionals of Wiener processes: exact asymptotics

We prove theorems on the exact asymptotics as T -> infinity of the integrals E inverted right perpendicular1/T integral(T)(0)vertical bar eta(t)vertical bar(p)dt inverted left perpendicular(-T), P > 0, for two stochastic processes xi(t), the Wiener process and the Brownian bridge, as well as for their conditional versions. We also obtain a number of related results. We shall use the Laplace method for the occupation times of homogeneous Markov processes. We write the constants in our exact asymptotic formulae explicitly in terms of the minimal eigenvalue and corresponding eigenfunction for the Schrodinger operator with a potential of polynomial type.