2015/09/01 by Hammer, Matthias, Ortgiese, Marcel, Völlering, Florian
#60H15 (Secondary) #60J80 #60K35 (Primary) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1509.00354
The symbiotic branching model is a spatial population model describing the dynamics of two interacting types that can only branch if both types are present. A classical result for the underlying stochastic partial differential equation identifies moments of the solution via a duality to a system of Brownian motions with dynamically changing colors. In this paper, we revisit this duality and give it a new interpretation. This new approach allows us to extend the duality to the limit as the branching rate γ is sent to infinity. This limit is particularly interesting since it captures the large scale behaviour of the system. As an application of the duality, we can explicitly identify the γ= ∞ limit when the driving noises are perfectly negatively correlated. The limit is a system of annihilating Brownian motions with a drift that depends on the initial imbalance between the types.