Presenting some recent results on the construction and the moments of Lévy-type processes the
focus of this volume is on a new existence theorem which is proved using a parametrix
construction. Applications range from heat kernel estimates for a class of Lévy-type processes
to existence and uniqueness theorems for Lévy-driven stochastic differential equations with
Hölder continuous coefficients. Moreover necessary and sufficient conditions for the existence
of moments of Lévy-type processes are studied and some estimates on moments are derived.
Lévy-type processes behave locally like Lévy processes but in contrast to Lévy processes they
are not homogeneous in space. Typical examples are processes with varying index of stability
and solutions of Lévy-driven stochastic differential equations. This is the sixth volume in a
subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a
number of important topics in the theory or applications of Lévy processes and pays tribute to
the state of the art of this rapidly evolving subject with special emphasis on the
non-Brownian world.
