We establish a duality relation for the moments of bounded solutions to a class of one-dimensional parabolic stochastic partial differential equations. The equations are driven by multiplicative space-time white noise, with a non-Lipschitz multiplicative functional. The dual process is a system of branching Brownian particles. The same method can be applied to show uniqueness in law for a class of non-Lipschitz finite dimensional stochastic differential equations.
"Uniqueness for a class of one-dimensional stochastic PDEs using moment duality." Ann. Probab. 28 (4) 1711 - 1734, October 2000. https://doi.org/10.1214/aop/1019160504