WIAS Preprint No. 822, (2003)

Compact interface property for symbiotic branching



Authors

  • Etheridge, Alison M.
  • Fleischmann, Klaus

2010 Mathematics Subject Classification

  • 60K35 60G57 60J80

Keywords

  • Symbiotic branching, mutually catalytic branching, stepping stone model, Anderson model, interacting superprocess, stochastic equation, collision localtime, self-dual, moment dual, moment equations, correlated noise, colourednoise, compact interface property, at most linear speed of propagation

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 finite at all times almost surely.

Appeared in

  • Stochastic Process. Appl., 114 (2004), pp. 127--160

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