Description
This volume presents recent developments in the area of Lvy-type processes and more general stochastic processes that behave locally like a Lvy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lvy-type process: a non-random function which is a counterpart of the characteristic exponent of a Lvy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levy-type processes. This is the third 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 applications of Lvy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. A Primer on Feller Semigroups and Feller Processes.- Feller Generators and Symbols.- Construction of Feller Processes.- Transformations of Feller Processes.- Sample Path Properties.- Global Properties.- Approximation.- Open Problems.- References.- Index.
