A NEW LOOK AT DUALITY FOR THE SYMBIOTIC BRANCHING MODEL

作者：Hammer Matthias^*; Ortgiese Marcel; Vollering Florian

来源：Annals of Probability, 2018, 46(5): 2800-2862.

DOI：10.1214/17-AOP1240

• Symbiotic branching model
• mutually catalytic branching
• stepping stone model
• rescaled interface
• moment duality
• annihilating Brownian motions

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 behavior of the system. As an application of the duality, we can explicitly identify the gamma = infinity 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.

• 出版日期2018-9