Quenched asymptotics for Brownian motion in generalized Gaussian potential

In this paper, we study the long-term asymptotics for the quenched moment Exexp{.t0V(Bs)ds} consisting of a d -dimensional Brownian motion {Bs;s.0} and a generalized Gaussian field V. The major progress made in this paper includes: Solution to an open problem posted by Carmona and Molchanov [Probab. Theory Related Fields 102 (1995) 433.453], the quenched laws for Brownian motions in Newtonian-type potentials and in the potentials driven by white noise or by fractional white noise.