Schilling, René L. / Partzsch, Lothar
An Introduction to Stochastic Processes
With contrib. by Böttcher, Björn
Series:De Gruyter Textbook
- 2nd revised and extended edition
- More than 200 exercises
- Solutions included
- For mathematicians, economists, engineers and scientists
Aims and Scope
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.
- xvi, 408 pages
- Type of Publication:
- Markov process; Transition semigroups; Brownian paths; Strassen’s functional law of the iterated logarithm; Skorokhod representation; Stochastic integrals; Itô’s formula; Stochastic differential equations