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We construct an unbiased estimator for function value evaluated at thesolution of a partial differential equation with random coefficients. We showthat the variance and expected computational cost of our estimator are finiteand our estimator is unsensitive to the problem dimension so that it can beapplied in problems across various disciplines. For the error analysis, weconnect the parabolic partial differential equations with the expectations ofstochastic differential equations and perform rough path estimation.

Unbiased Sampling of Multidimensional Partial Differential Equations with Random Coefficients