Stochastic Processes

From the reviews: "While this book is oriented toward students of physics, it could well be appreciated by a wider mathematical audience [ ] The text offers a rare opportunity to have a unified and modern treatment of stochastic processes in physics and finance." Bulletin of Mathematics BooksIn the canonical theoretical physics course starting with classical mechanics and electrodynamics we become used to deterministic thinking. Even quantum mechanics, although statistical in nature, is often presented from a deterministic point of view. It is not until we get into contact with statistical physics that probabilistic concepts enter into the physical world. Probabilities evolving in time, i.e., stochastic processes, are rarely treated, despite the wide - and interdisciplinary - applicability of the concepts. A diffusion process description applies in the classical Brownian motion problem, in path (-integral) descriptions of non-relativistic quantum mechanics as well as in the celebrated Black-Scholes theory of option pricing in the financial market. This book aims at providing the student with a self-contained introduction (from a physicists point of view) into the basic mathematical concepts of probability theory and stochastic processes and their application in physics and finance. Emphasis is laid onto contrasting the ubiquituous Gaussian distribution and standard Brownian motion with fat-tailed or Levy-stable distributions and Levy-flights, which are at the center of many modern developments in statistical physics as well as in econophysics.