LÚvy Matters III: LÚvy-Type Processes: Construction, Approximation and Sample Path Properties
This volume presents recent developments in the area of LÚvy-type processes and more general stochastic processes that behave locally like a LÚvy 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 LÚvy-type process: a non-random function which is a counterpart of the characteristic exponent of a LÚvy 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 LÚvy Matters. Each volume describes a number of important topics in the theory or applications of LÚvy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.