Anisotropic Operator Symbols Arising From Multivariate Jump Processes

作者：Reich Nils^*

来源：Integral Equations and Operator Theory, 2009, 63(1): 127-150.

DOI：10.1007/s00020-008-1645-y

• Integral operators
• symbol classes
• anisotropic Sobolev spaces
• Levy copulas
• jump processes
• sparse tensor products
• wavelet finite elements

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 Hormander-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.

• 出版日期2009-1