Levy processes form a wide and rich class of random process, and
have many applications ranging from physics to finance. Stochastic
calculus is the mathematics of systems interacting with random
noise. Here, the author ties these two subjects together, beginning
with an introduction to the general theory of Levy processes, then
leading on to develop the stochastic calculus for Levy processes in
a direct and accessible way. This fully revised edition now
features a number of new topics. These include: regular variation
and subexponential distributions; necessary and sufficient
conditions for Levy processes to have finite moments;
characterisation of Levy processes with finite variation; Kunita's
estimates for moments of Levy type stochastic integrals; new proofs
of Ito representation and martingale representation theorems for
general Levy processes; multiple Wiener-Levy integrals and chaos
decomposition; an introduction to Malliavin calculus; an
introduction to stability theory for Levy-driven SDEs.
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