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Over the past 10-15 years, we have seen a revival of general Levy '
processes theory as well as a burst of new applications. In the
past, Brownian motion or the Poisson process have been considered
as appropriate models for most applications. Nowadays, the need for
more realistic modelling of irregular behaviour of phen- ena in
nature and society like jumps, bursts, and extremeshas led to a
renaissance of the theory of general Levy ' processes. Theoretical
and applied researchers in elds asdiverseas
quantumtheory,statistical
physics,meteorology,seismology,statistics, insurance, nance, and
telecommunication have realised the enormous exibility of Lev ' y
models in modelling jumps, tails, dependence and sample path
behaviour. L' evy processes or Levy ' driven processes feature slow
or rapid structural breaks, extremal behaviour, clustering, and
clumping of points. Toolsandtechniquesfromrelatedbut disctinct
mathematical elds, such as point processes, stochastic
integration,probability theory in abstract spaces, and differ- tial
geometry, have contributed to a better understanding of Le 'vy jump
processes. As in many other elds, the enormous power of modern
computers has also changed the view of Levy ' processes. Simulation
methods for paths of Levy ' p- cesses and realisations of their
functionals have been developed. Monte Carlo simulation makes it
possible to determine the distribution of functionals of sample
paths of Levy ' processes to a high level of accuracy.
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