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The full history recursive multilevel Picard approximation method forsemilinear parabolic partial differential equations (PDEs) is the only methodwhich provably overcomes the curse of dimensionality for general time horizonsif the coefficient functions and the nonlinearity are globally Lipschitzcontinuous and the nonlinearity is gradient-independent. In this article weextend this result to locally monotone coefficient functions. Our results covera range of semilinear PDEs with polynomial coefficient functions.

Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions