Model Spaces of Regularity Structures for Space-Fractional SPDEs

@article{Berglund2017ModelSO,
  title={Model Spaces of Regularity Structures for Space-Fractional SPDEs},
  author={N. Berglund and C. K{\"u}hn},
  journal={Journal of Statistical Physics},
  year={2017},
  volume={168},
  pages={331-368}
}
  • N. Berglund, C. Kühn
  • Published 2017
  • Mathematics, Physics
  • Journal of Statistical Physics
  • We study model spaces, in the sense of Hairer, for stochastic partial differential equations involving the fractional Laplacian. We prove that the fractional Laplacian is a singular kernel suitable to apply the theory of regularity structures. Our main contribution is to study the dependence of the model space for a regularity structure on the three-parameter problem involving the spatial dimension, the polynomial order of the nonlinearity, and the exponent of the fractional Laplacian. The goal… CONTINUE READING
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