A general version of the Yamada-Watanabe and Engelbert results relating existence and uniqueness of strong and weak solutions for stochastic equations is given. The results apply to a wide variety of stochastic equations including classical stochastic differential equations, stochastic partial differential equations, and equations involving multiple time transformations.
"The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities." Electron. J. Probab. 12 951 - 965, 2007. https://doi.org/10.1214/EJP.v12-431