Uniqueness for a class of one-dimensional stochastic PDEs using moment duality. (English) Zbl 1044.60048

Summary: 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.


60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)


duality; uniqueness
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