Monte Carlo estimation of the solution of fractional partial\n differential equations

2020/12/27 by Vassili N. Kolokoltsov, Lin Feng, Kolokoltsov, Vassili +3 · 2 citations
Mathematics · #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2012.13904

Abstract

The paper is devoted to the numerical solutions of fractional PDEs based on\nits probabilistic interpretation, that is, we construct approximate solutions\nvia certain Monte Carlo simulations. The main results represent the upper bound\nof errors between the exact solution and the Monte Carlo approximation, the\nestimate of the fluctuation via the appropriate central limit theorem(CLT) and\nthe construction of confidence intervals. Moreover, we provide rates of\nconvergence in the CLT via Berry-Esseen type bounds. Concrete numerical\ncomputations and illustrations are included.\n

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