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Stochastic Processes for Physicists

Author: Kurt Jacobs

Publisher: Cambridge University Press

Published: 2010-02-18

Total Pages: 203

ISBN-13: 1139486799

Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.

An Introduction to Stochastic Processes in Physics

Author: Don S. Lemons

Publisher: Johns Hopkins University Press+ORM

Published: 2003-04-29

Total Pages: 165

ISBN-13: 0801876389

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This “lucid, masterfully written introduction to an often difficult subject . . . belongs on the bookshelf of every student of statistical physics” (Dr. Brian J. Albright, Applied Physics Division, Los Alamos National Laboratory). This book provides an accessible introduction to stochastic processes in physics and describes the basic mathematical tools of the trade: probability, random walks, and Wiener and Ornstein-Uhlenbeck processes. With an emphasis on applications, it includes end-of-chapter problems. Physicist and author Don S. Lemons builds on Paul Langevin’s seminal 1908 paper “On the Theory of Brownian Motion” and its explanations of classical uncertainty in natural phenomena. Following Langevin’s example, Lemons applies Newton’s second law to a “Brownian particle on which the total force included a random component.” This method builds on Newtonian dynamics and provides an accessible explanation to anyone approaching the subject for the first time. This volume contains the complete text of Paul Langevin’s “On the Theory of Brownian Motion,” translated by Anthony Gythiel.

Stochastic Processes in Physics and Chemistry

Author: N.G. Van Kampen

Publisher: Elsevier

Published: 1992-11-20

Total Pages: 482

ISBN-13: 0080571387

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This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.

Stochastic Processes in Science, Engineering and Finance

Author: Frank Beichelt

Publisher: CRC Press

Published: 2006-02-22

Total Pages: 438

ISBN-13: 9781420010459

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This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates their application by analyzing numerous practical examples. The treatment assumes few prerequisites, requiring only the standard mathematical maturity acquired by undergraduate applied science students. It includes an introductory chapter that summarizes the basic probability theory needed as background. Numerous exercises reinforce the concepts and techniques discussed and allow readers to assess their grasp of the subject. Solutions to most of the exercises are provided in an appendix. While focused primarily on practical aspects, the presentation includes some important proofs along with more challenging examples and exercises for those more theoretically inclined. Mastering the contents of this book prepares readers to apply stochastic modeling in their own fields and enables them to work more creatively with software designed for dealing with the data analysis aspects of stochastic processes.

Stochastic Processes in Physics and Engineering

Author: Sergio Albeverio

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 418

ISBN-13: 9400928939

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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. O. K. Chesterton. The Scandal of Father 'The Hermit Qad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Theory and Applications of Stochastic Processes

Author: Zeev Schuss

Publisher: Springer Science & Business Media

Published: 2009-12-09

Total Pages: 486

ISBN-13: 1441916059

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Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

Stochastic Processes and Applications

Author: Grigorios A. Pavliotis

Publisher: Springer

Published: 2014-11-19

Total Pages: 345

ISBN-13: 1493913239

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This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies 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. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Stochastic Processes in Mathematical Physics and Engineering

Author: American Mathematical Society

Publisher: American Mathematical Soc.

Published: 1964

Total Pages: 328

ISBN-13: 0821813161

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Physics of Stochastic Processes

Author: Reinhard Mahnke

Publisher: John Wiley & Sons

Published: 2009-08-04

Total Pages: 447

ISBN-13: 3527626107

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Based on lectures given by one of the authors with many years of experience in teaching stochastic processes, this textbook is unique in combining basic mathematical and physical theory with numerous simple and sophisticated examples as well as detailed calculations. In addition, applications from different fields are included so as to strengthen the background learned in the first part of the book. With its exercises at the end of each chapter (and solutions only available to lecturers) this book will benefit students and researchers at different educational levels. Solutions manual available for lecturers on www.wiley-vch.de

Discrete Stochastic Processes

Author: Robert G. Gallager

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 280

ISBN-13: 146152329X

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Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.