Nonlinear martingale problems in the McKean-Vlasov sense for superprocesses are studied. The stochastic calculus on historical trees is used in order to show that there is a unique solution of the nonlinear martingale problems under Lipschitz conditions on the coefficients.
"Nonlinear superprocesses." Ann. Probab. 24 (2) 743 - 760, April 1996. https://doi.org/10.1214/aop/1039639360