WIAS Preprint No. 641, (2001)

Mutually catalytic branching in the plane: Uniqueness


  • Dawson, Donald A.
  • Fleischmann, Klaus
  • Mytnik, Leonid
  • Perkins, Edwin A.
  • Xiong, Jie

2010 Mathematics Subject Classification

  • 60K35 60G57 60J80


  • Catalytic super-Brownian motion, collision local time, martingale problem, duality, uniqueness, Markov property




We study a pair of populations in ℝ2 which undergo diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the local density of the other type. Previous work had established the existence of such a process and derived some of its small scale and large scale properties. This paper is primarily focused on the proof of uniqueness of solutions to the martingale problem associated with the model. The self-duality property of solutions, which is crucial for proving uniqueness and was used in the previous work to derive many of the qualitative properties of the process, is also established.

Appeared in

  • Ann. Inst. H. Poincare Probab. Statist. 39(1) (2003), pp. 135-191

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