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Longtime Behaviour of Stochastic Hamiltonian Systems: The Multidimensional Case |
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| Authors: | Albeverio S. Klar A. |
| Affiliation: | (1) Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany;(2) Inst. Ang. Math., Universität Bonn, Wegelerstr. 6, D53115 Bonn, Germany SFB 237, Bochum-Essen-Düsseldorf; BiBoS Bielefeld; CERFIM Locarno, Switzerland;(3) Fachbereich Mathematik und Informatik, FU Berlin, D14195 Berlin, Germany |
| Abstract: | Hamiltonian systems perturbed by a white noise force are discussed in several dimensions. By using an appropriate scaling of the stochastic force a convergence theorem for the invariants of the deterministic motion is proved. This corresponds to convergence of the system to a stationary distribution. Especially motion in a central force field is considered; the energy and angular momentum processes are investigated. |
| Keywords: | Hamiltonian systems random perturbations stationary distribution invariants of motion nonlinear stochastic differential equations long time (asymptotic) behaviour multidimensional ergodic systems limit diffusions |
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