A Recursive Sparse Grid Collocation Method for Differential Equations with White Noise

@article{Zhang2014ARS,
  title={A Recursive Sparse Grid Collocation Method for Differential Equations with White Noise},
  author={Zhongqiang Zhang and Michael V. Tretyakov and Boris Rozovskii and George Em Karniadakis},
  journal={SIAM J. Sci. Comput.},
  year={2014},
  volume={36}
}
We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise. We first analyze the error of Smolyak's sparse grid collocation used to evaluate expectations of functionals of solutions to stochastic differential equations discretized by the Euler scheme. We show theoretically and numerically that this algorithm can have… Expand
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