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Author: Oliver C. Ibe
Publisher: John Wiley & Sons
ISBN: 1118618092
Category : Mathematics
Languages : en
Pages : 280
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Book Description
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.
Author: Oliver C. Ibe
Publisher: John Wiley & Sons
ISBN: 1118618092
Category : Mathematics
Languages : en
Pages : 280
Get Book Here
Book Description
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.
Author: Kwong-Tin Tang
Publisher:
ISBN:
Category : Matter
Languages : en
Pages : 84
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Book Description
Author: Joseph Rudnick
Publisher: Cambridge University Press
ISBN: 9781139450140
Category : Science
Languages : en
Pages : 350
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Book Description
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.
Author: Open University Course Team
Publisher:
ISBN: 9780749251680
Category : Diffusion
Languages : en
Pages : 200
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Book Description
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.
Author: George Herbert Weiss
Publisher: Elsevier Science & Technology
ISBN:
Category : Computers
Languages : en
Pages : 388
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Book Description
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
Author: Serguei Popov
Publisher: Cambridge University Press
ISBN: 1108472451
Category : Mathematics
Languages : en
Pages : 224
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Book Description
A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Author: Gregory F. Lawler
Publisher: Cambridge University Press
ISBN: 9780521519182
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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.
Author: Grigorios A. Pavliotis
Publisher: Springer
ISBN: 1493913239
Category : Mathematics
Languages : en
Pages : 345
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Book Description
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.
Author: Gregory F. Lawler
Publisher: American Mathematical Soc.
ISBN: 0821848291
Category : Mathematics
Languages : en
Pages : 170
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Book Description
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.
Author: Norman T. J. Bailey
Publisher: John Wiley & Sons
ISBN: 9780471523680
Category : Mathematics
Languages : en
Pages : 268
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Book Description
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.