Titlebook: Stochastic Processes; From Physics to Fina Wolfgang Paul,Jörg Baschnagel Book 2013Latest edition Springer International Publishing Switzerl

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,Beyond the Central Limit Theorem: Lévy Distributions,s fractal properties and super-diffusive behavior. Fractal time random walks and their relation to subdiffusive behavior are introduced next. Finally, we discuss the truncated Lévy flight which will be employed in Chap. . for the description of financial fluctuations.

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Modeling the Financial Market,évy flight as a possible model for real price fluctuations beyond the Gaussian assumption. We also discuss two recent agent based models for financial markets to identify possible mechanisms leading to the non-Gaussianity of financial markets. Finally an approach to model market crashes as a critical phenomenon is presented.

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stochastic processes in finance for natural scientists.PresThis 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 select

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A Brief Survey of the Mathematics of Probability Theory,ies as well as random variables are defined and examples for these mathematical structures in physics are given. The maximum entropy principle is presented as the basis to obtain a priori probabilities for a given problem. The central limit theorem is discussed and the theory of extreme value distri

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Diffusion Processes,blem and continuous time random walks. Then Brownian motion is analyzed in detail. We discuss the Kramers problem and exemplify the application of statistical and stochastic concepts to physics using the kinetic Ising model. Finally, following E. Nelson, we show how conservative diffusion processes

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A Brief Survey of the Mathematics of Probability Theory,butions is presented. For the theory of stochastic processes we focus on Markov processes and Martingales as these classes of processes underlie all applications discussed in later chapters. The master equation, the Fokker-Planck equation and Itô stochastic differential equations are discussed as the equations of motion for these processes.

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Diffusion Processes,can be described and that this description can be used as a foundation of quantum mechanics from which the Schrödinger equation can be derived. We apply this approach to the tunnel problem and to quantum field theory.