Potential Analysis

, Volume 12, Issue 3, pp 281–297 | Cite as

Longtime Behaviour of Stochastic Hamiltonian Systems: The Multidimensional Case

  • S. Albeverio
  • A. Klar


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.

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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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • S. Albeverio
    • 1
    • 2
  • A. Klar
    • 3
  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  2. 2.Inst. Ang. Math.Universität BonnBonnGermany SFB 237, Bochum-Essen-Düsseldorf; BiBoS Bielefeld; CERFIM Locarno, Switzerland
  3. 3.Fachbereich Mathematik und InformatikFU BerlinBerlinGermany

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