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Stochastic Processes and Applications
Diffusion Processes, the Fokker-Planck and Langevin Equations
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The purpose of this book is to present various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The focus is mostly on analytical techniques, although numerical and statistical techniques for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Some specific applications, such as stochastic resonance and Brownian motors are also discussed. The book is intended for beginning graduate students in these disciplines. Prerequisites include ordinary and partial differential equations, linear algebra, elementary functional analysis and techniques from applied mathematics such as perturbation theory. Basic knowledge of scientific computing and of a programming language or matlab would certainly be very helpful. Some familiarity with probability theory and stochastic processes in discrete time is also helpful but not essential.
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