For semilinear Kolmogorov PDEs with Lipschitz nonlinearities, a unique continuous at-most-polynomially-growing solution to the associated stochastic fixed point equation exists, even without a classical PDE solution.
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On existence and uniqueness properties for solutions of stochastic fixed point equations
For semilinear Kolmogorov PDEs with Lipschitz nonlinearities, a unique continuous at-most-polynomially-growing solution to the associated stochastic fixed point equation exists, even without a classical PDE solution.