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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. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.

Economics, Mathematical. --- Finance. --- Mathematical physics. --- Physics. --- Physics --- Physical Sciences & Mathematics --- Physics - General --- Stochastic processes. --- Probabilities. --- Probability --- Statistical inference --- Random processes --- Sociophysics. --- Econophysics. --- Economic theory. --- Socio- and Econophysics, Population and Evolutionary Models. --- Quantitative Finance. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Mathematical Methods in Physics. --- Mathematical Applications in the Physical Sciences. --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Probabilities --- Data-driven Science, Modeling and Theory Building. --- Funding --- Funds --- Economics --- Currency question --- Physical mathematics --- Economic theory --- Political economy --- Social sciences --- Economic man --- Economics, Mathematical . --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematical economics --- Econometrics --- Statistical physics --- Mathematical sociology --- Methodology --- Statistical methods

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Stochastic processes