EAN: 9783110307290

TEXTBOOK BROWNIAN MOTION - RENÉ L SCHILLING L...

Brownian motion is one of the most important stochastic processes in continuous time and with
continuous state space. Within the realm of stochastic processes  Brownian motion is at the
intersection of Gaussian processes  martingales  Markov processes  diffusions and random
fractals  and it has influenced the study of these topics. Its central position within
mathematics is matched by numerous applications in science  engineering and mathematical
finance. Often textbooks on probability theory cover  if at all  Brownian motion only briefly.
On the other hand  there is a considerable gap to more specialized texts on Brownian motion
which is not so easy to overcome for the novice. The authors' aim was to write a book which can
be used as an introduction to Brownian motion and stochastic calculus  and as a first course in
continuous-time and continuous-state Markov processes. They also wanted to have a text which
would be both a readily accessible mathematical back-up for contemporary applications (such as
mathematical finance) and a foundation to get easy access to advanced monographs. This textbook
tailored to the needs of graduate and advanced undergraduate students  covers Brownian motion 
starting from its elementary properties  certain distributional aspects  path properties  and
leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for
the simulation of Brownian motion.

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