Symmetric Lévy type operator
The paper presents some sufficient conditions for the existence of a symmetric measure for a Lévy type operator: \[ \begin{multlined} L f (x) = \sum _ {i, j = 1}^ {d} a_ {i j} (x) \partial _ {i j} f(x) + \sum _ {i=1}^ {d} b_ {i} (x) \partial _ {i} f(x) + \int _ {\mathbb{R}^ {d} \setminus \{ 0 \}}\\ \left ( f(x+z) - f(x) - {\mathbf 1}_ {|z| \leq 1} \sum _ {i=1}^ {d} z_ {i} \partial _ {i} f(x) \right ) \nu (x, d z)\end{multlined} \] where: \((a_ {i j}(x))\) is non-negative definite matrix of functions of class \({\mathcal C}^ {2}\); \((b_ {i}(x))\) a vector of measurable functions and \(\nu (x, d z)\) is a Lévy jump measure kernel.
scientific article; zbMATH DE number 5629481