Journal of Theoretical Probability

, Volume 8, Issue 1, pp 179–206

Super-Brownian motions in higher dimensions with absolutely continuous measure states

  • Donald A. Dawson
  • Klaus Fleischmann

DOI: 10.1007/BF02213461

Cite this article as:
Dawson, D.A. & Fleischmann, K. J Theor Probab (1995) 8: 179. doi:10.1007/BF02213461


Continuous super-Brownian motions in two and more dimensions are known to have singular measure states. However, by weakening the branching mechanism in an irregular way they can be forced to have absolutely continuous states. The sufficient conditions we impose are identified in a couple of examples with irregularities in only one coordinate. This includes the case of branching restricted to some densely situated ensemble of hyperplanes.

Key Words

Catalytic medium random medium fundamental solution superprocess branching rate functional 

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Donald A. Dawson
    • 1
  • Klaus Fleischmann
    • 2
  1. 1.Department of Mathematics and StatisticsCarleton UniversityCanada
  2. 2.Weierstrass-Institute for Applied Analysis and StochasticsBerlinGermany

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