  The existence of global nonnegative martingale solutions to cross-diffusion
systems of Shigesada-Kawasaki-Teramoto type with multiplicative noise is
proven. The model describes the stochastic segregation dynamics of an arbitrary
number of population species in a bounded domain with no-flux boundary
conditions. The diffusion matrix is generally neither symmetric nor positive
semidefinite, which excludes standard methods for evolution equations. Instead,
the existence proof is based on the entropy structure of the model, a novel
regularization of the entropy variable, higher-order moment estimates, and
fractional time regularity. The regularization technique is generic and is
applied to the population system with self-diffusion in any space dimension and
without self-diffusion in two space dimensions.
