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Anisotropic operator symbols arising from multivariate jump processes

by N. Reich

(Report number 2008-25)

Abstract
It is shown that infinitesimal generators of certain multivariate pure jump Lévy copula processes give rise to a class of anisotropic symbols that extends the well-known classes of pseudodifferential operators of Hörmander-type. In addition, we provide minimal regularity convergence analysis for a sparse tensor product finite element approximation to solutions of the corresponding stationary Kolmogorov equations. The computational complexity of the presented approximation scheme is essentially independent of the underlying state space dimension.

Keywords:

@Techreport{R08_389,
  author = {N. Reich},
  title = {Anisotropic operator symbols arising from multivariate jump processes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-25},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-25.pdf },
  year = {2008}
}

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