TY - JOUR

T1 - The rate of escape for some Gaussian processes and the scattering theory for their small perturbations

AU - Albeverio, S

AU - Kolokoltsov, VN

PY - 1997/5/16

Y1 - 1997/5/16

N2 - A detailed estimate on the growth of the position coordinate in a nonlinearly perturbed Ornstein-Uhlenbeck phase process is given in all dimensions d greater than or equal to 3. The corresponding stochastic wave operators are constructed. A corresponding asymptotics of the phase space process for stochastically perturbed oscillator processes, and systems of semilinear stochastic differential equations with nondiagonal constant diffusion matrix is also studied, Extensions to infinite dimensional cases (stochastically perturbed wave equation and Schrodinger equations) are given.

AB - A detailed estimate on the growth of the position coordinate in a nonlinearly perturbed Ornstein-Uhlenbeck phase process is given in all dimensions d greater than or equal to 3. The corresponding stochastic wave operators are constructed. A corresponding asymptotics of the phase space process for stochastically perturbed oscillator processes, and systems of semilinear stochastic differential equations with nondiagonal constant diffusion matrix is also studied, Extensions to infinite dimensional cases (stochastically perturbed wave equation and Schrodinger equations) are given.

KW - stochastic wave operators

KW - asymptotics

KW - non-linear stochastic processes

KW - stochastically perturbed Schrodinger equations

KW - INVARIANT-MEASURES

KW - RECURRENCE

KW - DIFFUSIONS

U2 - 10.1016/S0304-4149(97)00013-6

DO - 10.1016/S0304-4149(97)00013-6

M3 - статья

VL - 67

SP - 139

EP - 159

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 2

ER -