This volume presents recent developments in the area of
Levy-type processes and more general stochastic processes that
behave locally like a Levy 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
Levy-type process: a non-random function which is a counterpart of
the characteristic exponent of a Levy 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 Levy Matters. Each volume describes a number of
important topics in the theory or applications of Levy 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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