L’vy Matters VI
L’vy-Type Processes: Moments, Construction and Heat Kernel EstimatesPresenting 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. ISBN: 9783319608877, 3319608878
