Basic Stochastic Processes

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included.

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included.

These proceedings are based on lectures delivered at the School. The aim was to introduce research workers at the pre- and post-doctoral levels to the basic concepts, techniques and applications of stochastic theories. Some of the discussions, such as those on the properties of Gaussian and Markov processes and on Langevin and Fokker-Planck equations, have by now become standard textbook material. It