Preface
Brownian motion is arguably the single most important stochastic process. Historically it was the first stochastic process in continuous time and with a continuous state space, and thus it influenced the study of Gaussian processes, martingales, Markov processes, diffusions and random fractals. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance.
The present book grew out of several courses which we taught at the University of Marburg and TU Dresden, and it draws on the lecture notes [172] by one of us. Many students are interested in applications of probability theory and it is important to teach Brownian motion and stochastic calculus at an early stage of the ...
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