THE RATE OF ESCAPE FOR SOME GAUSSIAN-PROCESSES AND THE SCATTERING-THEORY FOR THEIR SMALL PERTURBATIONS

A detailed estimate on the growth of the position coordinate in a nonl inearly perturbed Ornstein-Uhlenbeck phase process is given in all dim ensions d greater than or equal to 3. The corresponding stochastic wav e operators are constructed. A corresponding asymptotics of the phase space process for stochastically perturbed oscillator processes, and s ystems of semilinear stochastic differential equations with nondiagona l constant diffusion matrix is also studied, Extensions to infinite di mensional cases (stochastically perturbed wave equation and Schrodinge r equations) are given.