Compact interface property for symbiotic branching

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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.

MSC

primary 60K35
secondary 60G57
60J80

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

Cited by (0)

1

AME is supported by an EPSRC Advanced Fellowship.

2

KF is partly supported by the research program “Interacting Systems of High Complexity” of the German Science Foundation.