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Monte Carlo Estimation of the Solution of Fractional Partial Differential Equations

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FD2W03 - Optimal control and fractional dynamics

The paper is devoted to the numerical solutions of fractional PDEsbased on its probabilistic interpretation, that is, we construct approximatesolutions via certain Monte Carlo simulations. The main results representthe upper bound of errors between the exact solution and the Monte Carloapproximation, the estimate of the fluctuation via the appropriate centrallimit theorem (CLT) and the construction of confidence intervals. More-over, we provide rates of convergence in the CLT via Berry-Esseen typebounds. Concrete numerical computations and illustrations are included.

This talk is part of the Isaac Newton Institute Seminar Series series.

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