A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs

@inproceedings{Fahim2011APN,
  title={A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs},
  author={Arash Fahim and Nizar Touzi and Xavier Warin},
  year={2011}
}
We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in [12], and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretization error in terms of the time step. An explicit implementable scheme requires to approximate the… CONTINUE READING

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