We study the limiting behavior of large branching particle systems undergoing random motion, whose branching mechanism is affected by a random environment. The weak convergence result is established for a sequence of such particle systems and the limiting process is characterized as the unique solution of a martingale problem. The proof of uniqueness of the solution for the martingale problem requires an extension of standard duality techniques.
"Superprocesses in random environments." Ann. Probab. 24 (4) 1953 - 1978, October 1996. https://doi.org/10.1214/aop/1041903212