  The existence of global nonnegative martingale solutions to a cross-diffusion
system of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven.
The model describes the segregation dynamics of populations with an arbitrary
number of species. The diffusion matrix is generally neither symmetric nor
positive semidefinite, which excludes standard methods. Instead, the existence
proof is based on the entropy structure of the model, approximated by a
Wong-Zakai argument, and on suitable higher moment estimates and fractional
time regularity. In the case without self-diffusion, the lack of regularity is
overcome by carefully exploiting the entropy production terms.
