Stochastic Methods for Solving High-Dimensional Partial Differential Equations

@article{BillaudFriess2018StochasticMF,
  title={Stochastic Methods for Solving High-Dimensional Partial Differential Equations},
  author={Marie Billaud-Friess and Arthur Macherey and Anthony Nouy and Cl{\'e}mentine Prieur},
  journal={arXiv: Numerical Analysis},
  year={2018}
}
We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms… Expand
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