On convergence of population processes in random environments to the stochastic heat equation with colored noise

We consider the stochastic heat equation with a multiplicative colored noise term on Rd for d ≥ 1. First, we prove convergence of a branching particle system in a random environment to this stochastic heat equation with linear noise coefficients. For this stochastic partial differential equation with more general non-Lipschitz noise coefficients we show… (More)