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Compact interface property for symbiotic branching

Author

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  • Etheridge, Alison M.
  • Fleischmann, Klaus

Abstract

A process which we call symbiotic branching, is suggested covering three well-known interacting models: mutually catalytic branching, the stepping stone model, and the Anderson model. Basic tools such as self-duality, particle system moment duality, measure case moment duality, and moment equations are still available in this generalized context. As an application, we show that in the setting of the one-dimensional continuum the compact interface property holds: starting from complementary Heaviside states, the interface is compact at each time almost surely and propagates at most with a linear speed.

Suggested Citation

  • Etheridge, Alison M. & Fleischmann, Klaus, 2004. "Compact interface property for symbiotic branching," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 127-160, November.
    • Handle: RePEc:eee:spapps:v:114:y:2004:i:1:p:127-160
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    Cited by:

    1. Dawson, Donald A. & Fleischmann, Klaus & Xiong, Jie, 2005. "Strong uniqueness for cyclically symbiotic branching diffusions," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 251-257, July.

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