WIAS Preprint No. 135, (1994)

Comparison of interacting diffusions and an application to their ergodic theory


  • Cox, J. Theodore
  • Fleischmann, Klaus
  • Greven, Andreas

2010 Mathematics Subject Classification

  • 60K35 60J60 60J15


  • comparison arguments, interacting diffusion, interacting particle system, clustering




A general comparison argument for expectations of certain multi-time functionals of infnite systems of linearly interacting diffusions differing in the diffusion coeffcient is derived. As an application we prove clustering occurs in the case when the symmetrized interaction kernel is recurrent, and the components take values in an interval bounded on one side. The technique also gives an alternative proof of clustering in the case of compact intervals.

Appeared in

  • Probab. Theory Relat. Fields, 105 (1996), pp. 513-528

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