Compact interface property for symbiotic branching

Alison M. Etheridge and Klaus Fleischmann

Stochastic Processes and their Applications, 2004, vol. 114, issue 1, 127-160

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.

Keywords: Symbiotic; branching; Mutually; catalytic; branching; Stepping; stone; model; Anderson; model; Interacting; superprocess; Stochastic; equation; Collision; local; time; Self-dual; Moment; dual; Moment; equations; Correlated; noise; Coloured; noise; Compact; interface; property; At; most; linear; speed; of; propagation; Rightmost; point; of; support (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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