• DOI:10.1214/17-AOP1240
• Corpus ID: 13684988

A new look at duality for the symbiotic branching model

@article{Hammer2018ANL,
  title={A new look at duality for the symbiotic branching model},
  author={Matthias Hammer and Marcel Ortgiese and Florian Vollering},
  journal={The Annals of Probability},
  year={2018}
}

• Matthias Hammer, Marcel Ortgiese, F. Vollering
• Published 1 September 2015
• Mathematics
• The Annals of Probability

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 $\gamma$ 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 $\gamma = \infty$ 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.