Anisotropic Operator Symbols Arising From Multivariate Jump Processes

摘要

It is shown that infinitesimal generators A of certain multivariate pure jump Levy copula processes give rise to a class of anisotropic symbols that extends the well-known classes of pseudo differential operators of H_rmander-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 Au = f.The computational complexity of the presented approximation scheme is essentially independent of the underlying state space dimension.