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On Changes of Measure for Super Brownian Motion

Author

Listed:
  • Robert J. Adler

    (Technion)

  • Srikanth K. Iyer

    (Indian Institute of Technology)

Abstract

Let η be a superprocess under the measure P. We show the existence of probability measures which are absolutely continuous with respect to P, and whose Randon–Nikodym derivatives are suitably normalized functions of the self intersection local time of η. These measures correspond to measure valued processes exhibiting a certain amount of (reinforcing) self interaction in terms of both the particle motion and the branching mechanism.

Suggested Citation

  • Robert J. Adler & Srikanth K. Iyer, 2001. "On Changes of Measure for Super Brownian Motion," Journal of Theoretical Probability, Springer, vol. 14(2), pages 527-557, April.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:2:d:10.1023_a:1011124000185
    DOI: 10.1023/A:1011124000185
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    References listed on IDEAS

    as
    1. Adler, Robert J. & Iyer, Srikanth K., 1997. "Attractive polymer models for two- and three-dimensional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 271-281, March.
    2. Feldman, Raisa E. & Iyer, Srikanth K., 1996. "A representation for functionals of superprocesses via particle picture," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 173-186, November.
    3. Robert Adler & Roger Tribe, 1998. "Uniqueness for a Historical SDE with a Singular Interaction," Journal of Theoretical Probability, Springer, vol. 11(2), pages 515-533, April.
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