Lvy Matters VI

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