02474nam a22003615i 4500991003575589707536m o d cr cnu|||unuuu181123s2017 sz a ob 001 0 eng d9783319608884978331960887710.1007/978-3-319-60888-4doib14354135-39ule_inst519.223AMS 60G51Kühn, Franziska755752Lévy Matters VI[e-book] :Lévy-Type Processes: Moments, Construction and Heat Kernel Estimates /by Franziska KühnCham :Springer,20171 online resource (xxiii, 245 p. 39 illus., 1 illus. in color.)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture Notes in Mathematics,0075-8434 ;2187Presenting 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 applicati ons of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject, with special emphasis on the non-Brownian worldDifferential equations, PartialProbabilitiesPrinted edition:9783319608877https://link.springer.com/book/10.1007/978-3-319-60888-4An electronic book accessible through the World Wide Web.b1435413503-03-2223-11-18991003575589707536Lévy Matters VI1749307UNISALENTOle01323-11-18m@ -engsz 00