The aim of this book is to provide a straightforward and accessible introduction
to stochastic integrals and stochastic differential equations driven by L′evy
processes.
L′evy processes are essentially stochastic processes with stationary and independent
increments. Their importance in probability theory stems from the
following facts:
• they are analogues of random walks in continuous time;
• they form special subclasses of both semimartingales and Markov processes
for which the analysis is on the one hand much simpler and on the other
hand provides valuable guidance for the general case;
• they are the simplest examples of random motion whose sample paths are
right-continuous and have a number (at most countable) of random jump
discontinuities occurring at random times, on each finite time interval.
• they include a number of very important processes as special cases, including
Brownian motion, the Poisson process, stable and self-decomposable
processes and subordinators.