Compact interface property for symbiotic branching
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.
Year of publication: |
2004
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Authors: | Etheridge, Alison M. ; Fleischmann, Klaus |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 114.2004, 1, p. 127-160
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Publisher: |
Elsevier |
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 |
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