The solution of a random semilinear hyperbolic system with singular initial data is sought as a random Colombeau distribution. The product of 2 additive white noises is well tackled within the theory of random Colombeau distributions. In the special case of a random predator--prey system, the exact Colombeau solution is obtained under some assumptions when the process is driven by doubly reflected Brownian motions.
"Colombeau solutions of a nonlinear stochastic predator--prey equation,"
Turkish Journal of Mathematics: Vol. 37:
6, Article 15.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss6/15