Download or read book Elements of Random Walk and Diffusion Processes written by Oliver C. Ibe and published by John Wiley & Sons. This book was released on 2013-09-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes. With a strong emphasis on the relationship between random walk theory and diffusion processes, Elements of Random Walk and Diffusion Processes features: Basic concepts in probability, an overview of stochastic and fractional processes, and elements of graph theory Numerous practical applications of random walk across various disciplines, including how to model stock prices and gambling, describe the statistical properties of genetic drift, and simplify the random movement of molecules in liquids and gases Examples of the real-world applicability of random walk such as node movement and node failure in wireless networking, the size of the Web in computer science, and polymers in physics Plentiful examples and exercises throughout that illustrate the solution of many practical problems Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques.
Download or read book Elements of the Random Walk written by Joseph Rudnick and published by Cambridge University Press. This book was released on 2004-03-04 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.
Download or read book Aspects and Applications of the Random Walk written by George Herbert Weiss and published by Elsevier Science & Technology. This book was released on 1994 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paperback. Both the formalism and many of the attendant ideas related to the random walk lie at the core of a significant fraction of contemporary research in statistical physics. In the language of physics the random walk can be described as a microscopic model for transport processes which have some element of randomness. The starting point of nearly all analyses of transport in disordered media is to be found in one or another type of random walk model. Mathematical formalism based on the theory of random walks is not only pervasive in a number of areas of physics, but also finds application in many areas of chemistry. The random walk has also been applied to the study of a number of biological phenomena.Despite the obvious importance of random walks in these and other applications there are few books devoted to the subject. This is therefore a timely introduction to the subject which will be welcomed by students and more senior researchers who have
Download or read book Two Dimensional Random Walk written by Serguei Popov and published by Cambridge University Press. This book was released on 2021-03-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Download or read book Random Walks and Diffusion written by Open University Course Team and published by . This book was released on 2009-10-21 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This block explores the diffusion equation which is most commonly encountered in discussions of the flow of heat and of molecules moving in liquids, but diffusion equations arise from many different areas of applied mathematics. As well as considering the solutions of diffusion equations in detail, we also discuss the microscopic mechanism underlying the diffusion equation, namely that particles of matter or heat move erratically. This involves a discussion of elementary probability and statistics, which are used to develop a description of random walk processes and of the central limit theorem. These concepts are used to show that if particles follow random walk trajectories, their density obeys the diffusion equation.
Download or read book Random Walk A Modern Introduction written by Gregory F. Lawler and published by Cambridge University Press. This book was released on 2010-06-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
Download or read book The Elements of Stochastic Processes with Applications to the Natural Sciences written by Norman T. J. Bailey and published by John Wiley & Sons. This book was released on 1991-01-16 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops an introductory and relatively simple account of the theory and application of the evolutionary type of stochastic process. Professor Bailey adopts the heuristic approach of applied mathematics and develops both theoretical principles and applied techniques simultaneously.
Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Random Walk and the Heat Equation written by Gregory F. Lawler and published by American Mathematical Soc.. This book was released on 2010-11-22 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.
Download or read book Statistical Mechanics and Random Walks written by Abram Skogseid and published by . This book was released on 2011-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors gather and present topical research in the study of statistical mechanics and random walk principles and applications. Topics discussed in this compilation include the application of stochastic approaches to modelling suspension flow in porous media; subordinated Gaussian processes; random walk models in biophysical science; non-equilibrium dynamics and diffusion processes; global random walk algorithm for diffusion processes and application of random walks for the analysis of graphs, musical composition and language phylogeny.
Download or read book Elements of the Theory of Markov Processes and Their Applications written by A. T. Bharucha-Reid and published by Courier Corporation. This book was released on 2012-04-26 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition.
Download or read book Basic Theory written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
Download or read book Elements of the Random Walk written by Joseph Rudnick and published by Cambridge University Press. This book was released on 2004-03-04 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. This book is an introduction to some of the most powerful and general techniques used in the application of these ideas. Its self-contained text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.
Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Download or read book Non homogeneous Random Walks written by Mikhail Menshikov and published by Cambridge University Press. This book was released on 2016-12-22 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.
Download or read book Statistical Mechanics and Random Walks written by Abram Skogseid and published by Nova Science Publishers. This book was released on 2012-02-01 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors gather and present topical research in the study of statistical mechanics and random walk principles and applications. Topics discussed in this compilation include the application of stochastic approaches to modelling suspension flow in porous media; subordinated Gaussian processes; random walk models in biophysical science; non-equilibrium dynamics and diffusion processes; global random walk algorithm for diffusion processes and application of random walks for the analysis of graphs, musical composition and language phylogeny.
Download or read book Fundamentals of Stochastic Networks written by Oliver C. Ibe and published by John Wiley & Sons. This book was released on 2011-08-24 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: An interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physical sciences. The author uniquely unites different types of stochastic, queueing, and graphical networks that are typically studied independently of each other. With balanced coverage, the book is organized into three succinct parts: Part I introduces basic concepts in probability and stochastic processes, with coverage on counting, Poisson, renewal, and Markov processes Part II addresses basic queueing theory, with a focus on Markovian queueing systems and also explores advanced queueing theory, queueing networks, and approximations of queueing networks Part III focuses on graphical models, presenting an introduction to graph theory along with Bayesian, Boolean, and random networks The author presents the material in a self-contained style that helps readers apply the presented methods and techniques to science and engineering applications. Numerous practical examples are also provided throughout, including all related mathematical details. Featuring basic results without heavy emphasis on proving theorems, Fundamentals of Stochastic Networks is a suitable book for courses on probability and stochastic networks, stochastic network calculus, and stochastic network optimization at the upper-undergraduate and graduate levels. The book also serves as a reference for researchers and network professionals who would like to learn more about the general principles of stochastic networks.
