Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.23969 |
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Inhaltsangabe:
- Full history recursive multilevel Picard (MLP) approximations have been proved to overcome the curse of dimensionality in the numerical approximation of semilinear heat equations with nonlinearities which are globally Lipschitz continuous with respect to the maximum-norm. Nonlinearities in Hamilton-Jacobi-Bellman equations in stochastic control theory, however, are often (locally) Lipschitz continuous with respect to the standard Euclidean norm. In this paper we prove the surprising fact that MLP approximations for one such example equation suffer from the curse of dimensionality.