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 ...
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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.
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