  In several examples, dualities for interacting diffusion and particle systems
permit the study of the longtime behavior of solutions. A particularly
difficult model in which many techniques collapse is a two-type model with
mutually catalytic interaction introduced by Dawson/Perkins for which they
proved under some assumptions a dichotomy between extinction and coexistence
directly from the defining equations. In the present article we show how to
prove a precise dichotomy for a related model with negatively correlated
noises. The proof uses moment bounds on exit-times of correlated Brownian
motions from the first quadrant and explicit second moment calculations. Since
the uniform integrability bound is independent of the branching rate our proof
can be extended to infinite branching rate processes.

Probability