Lévy Matters VI: Lévy-Type Processes: Moments, Construction and Heat Kernel Estimates

By Franziska Kühn

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

• Format: Paperback
• Language: English
• ISBN: 3319608878
• ISBN13: 9783319608877
• Release Date: October 2017
• Publisher: Springer
• Length: 245 Pages
• Weight: 0.85 lbs.
• Dimensions: 0.6" x 6.1" x 9.2"