Elements of the Random Walk

Author: Joseph Rudnick
Publisher: Cambridge University Press
ISBN: 9781139450140
Format: PDF
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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.

Fractional order Modeling of Nuclear Reactor From Subdiffusive Neutron Transport to Control oriented Models

Author: Vishwesh Vyawahare
Publisher: Springer
ISBN: 9811075875
Format: PDF, Mobi
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This book addresses the topic of fractional-order modeling of nuclear reactors. Approaching neutron transport in the reactor core as anomalous diffusion, specifically subdiffusion, it starts with the development of fractional-order neutron telegraph equations. Using a systematic approach, the book then examines the development and analysis of various fractional-order models representing nuclear reactor dynamics, ultimately leading to the fractional-order linear and nonlinear control-oriented models. The book utilizes the mathematical tool of fractional calculus, the calculus of derivatives and integrals with arbitrary non-integer orders (real or complex), which has recently been found to provide a more compact and realistic representation to the dynamics of diverse physical systems. Including extensive simulation results and discussing important issues related to the fractional-order modeling of nuclear reactors, the book offers a valuable resource for students and researchers working in the areas of fractional-order modeling and control and nuclear reactor modeling.

Complex Networks

Author: Luciano da F. Costa
Publisher: Springer
ISBN: 3642255019
Format: PDF, Kindle
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This book constitutes the thoroughly refereed post-conference proceedings of the Second International Workshop on Complex Networks, CompleNet 2010, which was held in Rio de Janeiro, Brazil, in October 2010. The 21 revised papers presented were carefully reviewed and selected from 48 submissions. The topics covered include: community structure, network metrics, network models, effect of topology to epidemics, algorithms to classify networks, self-organized algorithms applied to complex networks, as well as many applications of complex networks in biology, image analysis, software development, traffic congestion, language and speech, sensor networks, and synchronization.

Elements of Random Walk and Diffusion Processes

Author: Oliver C. Ibe
Publisher: John Wiley & Sons
ISBN: 1118617932
Format: PDF, Docs
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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.

Random Walks in Biology

Author: Howard C. Berg
Publisher: Princeton University Press
ISBN: 9780691000640
Format: PDF, Mobi
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This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.

Aspects and applications of the random walk

Author: George Herbert Weiss
Publisher: North Holland
ISBN: 9780444816061
Format: PDF
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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 had no prior contact with the field. The author has focussed on simpler aspects of the subject, focussing mainly on Markovian models, or models closely related to a Markovian formulation. Such models are exemplified by the continuous-time random walk which has both Markovian and non-Markovian aspects. Considerable emphasis has been placed on asymptotic properties of random walks because their universal properties are the ones that permit such a wide range of applications of the mathematical formalism. Attention is also given to an introductory account of Abelian and Tauberian theorems.

Random Walk A Modern Introduction

Author: Gregory F. Lawler
Publisher: Cambridge University Press
ISBN: 1139488767
Format: PDF, ePub, Mobi
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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.

A Non Random Walk Down Wall Street

Author: Andrew W. Lo
Publisher: Princeton University Press
ISBN: 1400829097
Format: PDF
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For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. Here Andrew W. Lo and A. Craig MacKinlay put the Random Walk Hypothesis to the test. In this volume, which elegantly integrates their most important articles, Lo and MacKinlay find that markets are not completely random after all, and that predictable components do exist in recent stock and bond returns. Their book provides a state-of-the-art account of the techniques for detecting predictabilities and evaluating their statistical and economic significance, and offers a tantalizing glimpse into the financial technologies of the future. The articles track the exciting course of Lo and MacKinlay's research on the predictability of stock prices from their early work on rejecting random walks in short-horizon returns to their analysis of long-term memory in stock market prices. A particular highlight is their now-famous inquiry into the pitfalls of "data-snooping biases" that have arisen from the widespread use of the same historical databases for discovering anomalies and developing seemingly profitable investment strategies. This book invites scholars to reconsider the Random Walk Hypothesis, and, by carefully documenting the presence of predictable components in the stock market, also directs investment professionals toward superior long-term investment returns through disciplined active investment management.

A Random Walk Down Wall Street The Time Tested Strategy for Successful Investing Eleventh Edition

Author: Burton G. Malkiel
Publisher: W. W. Norton & Company
ISBN: 039324895X
Format: PDF, ePub
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The best investment guide money can buy, with over 1.5 million copies sold, now fully revised and updated. In today’s daunting investment landscape, the need for Burton G. Malkiel’s reassuring, authoritative, and perennially best-selling guide to investing is stronger than ever. A Random Walk Down Wall Street has long been established as the first book to purchase when starting a portfolio. This new edition features fresh material on exchange-traded funds and investment opportunities in emerging markets; a brand-new chapter on “smart beta” funds, the newest marketing gimmick of the investment management industry; and a new supplement that tackles the increasingly complex world of derivatives.