Aspects And Applications Of The Random Walk

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Aspects and Applications of the Random Walk

Author : George Herbert Weiss
Publisher : Elsevier Science & Technology
ISBN 13 :
Total Pages : 388 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Aspects and Applications of the Random Walk by : George Herbert Weiss

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

Two-Dimensional Random Walk

Author : Serguei Popov
Publisher : Cambridge University Press
ISBN 13 : 1108472451
Total Pages : 224 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Two-Dimensional Random Walk by : Serguei Popov

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.

Dynamic Random Walks

Author : Nadine Guillotin-Plantard
Publisher : Elsevier
ISBN 13 : 0080462847
Total Pages : 279 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Dynamic Random Walks by : Nadine Guillotin-Plantard

Download or read book Dynamic Random Walks written by Nadine Guillotin-Plantard and published by Elsevier. This book was released on 2006-02-08 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!). · New probabilistic model, new results in probability theory · Original applications in computer science · Applications in mathematical physics · Applications in finance

Elements of the Random Walk

Author : Joseph Rudnick
Publisher : Cambridge University Press
ISBN 13 : 9781139450140
Total Pages : 350 pages
Book Rating : 4.4/5 (51 download)

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Book Synopsis Elements of the Random Walk by : Joseph Rudnick

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.

An Unbounded Experience In Random Walks With Applications

Author : Michael F Shlesinger
Publisher : World Scientific
ISBN 13 : 9811232822
Total Pages : 214 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis An Unbounded Experience In Random Walks With Applications by : Michael F Shlesinger

Download or read book An Unbounded Experience In Random Walks With Applications written by Michael F Shlesinger and published by World Scientific. This book was released on 2021-06-29 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the author's account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul Lévy's work via Mandelbrot's Lévy flights which are featured uniquely as Weierstrass and Riemann random walks.Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green's functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made to anomalous diffusion and conductivity in amorphous semiconductors and supercooled liquids. The glass transition is discussed especially for pressure effects.All along the way, personal stories are recounted and special appreciations are made to Elliott Montroll and Harvey Scher for their ever-expanding influence on the field of non-equilibrium anomalous processes that now are found in topics including disordered materials, water table processes, animal foraging, blinking quantum dots, rotating flows, optical lattices, dynamical strange attractors and strange kinetics.

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing (Ninth Edition)

Author : Burton G. Malkiel
Publisher : W. W. Norton & Company
ISBN 13 : 0393330338
Total Pages : 454 pages
Book Rating : 4.3/5 (933 download)

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Book Synopsis A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing (Ninth Edition) by : Burton G. Malkiel

Download or read book A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing (Ninth Edition) written by Burton G. Malkiel and published by W. W. Norton & Company. This book was released on 2007-12-17 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updated with a new chapter that draws on behavioral finance, the field that studies the psychology of investment decisions, the bestselling guide to investing evaluates the full range of financial opportunities.

Random Walks on Infinite Graphs and Groups

Author : Wolfgang Woess
Publisher : Cambridge University Press
ISBN 13 : 0521552923
Total Pages : 350 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Random Walks on Infinite Graphs and Groups by : Wolfgang Woess

Download or read book Random Walks on Infinite Graphs and Groups written by Wolfgang Woess and published by Cambridge University Press. This book was released on 2000-02-13 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.

Random and Restricted Walks

Author : Michael N. Barber
Publisher : CRC Press
ISBN 13 : 9780677026206
Total Pages : 190 pages
Book Rating : 4.0/5 (262 download)

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Book Synopsis Random and Restricted Walks by : Michael N. Barber

Download or read book Random and Restricted Walks written by Michael N. Barber and published by CRC Press. This book was released on 1970 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Future Perspectives in Risk Models and Finance

Author : Alain Bensoussan
Publisher : Springer
ISBN 13 : 3319075241
Total Pages : 315 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Future Perspectives in Risk Models and Finance by : Alain Bensoussan

Download or read book Future Perspectives in Risk Models and Finance written by Alain Bensoussan and published by Springer. This book was released on 2014-11-20 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a perspective on a number of approaches to financial modelling and risk management. It examines both theoretical and practical issues. Theoretically, financial risks models are models of a real and a financial “uncertainty”, based on both common and private information and economic theories defining the rules that financial markets comply to. Financial models are thus challenged by their definitions and by a changing financial system fueled by globalization, technology growth, complexity, regulation and the many factors that contribute to rendering financial processes to be continuously questioned and re-assessed. The underlying mathematical foundations of financial risks models provide future guidelines for risk modeling. The book’s chapters provide selective insights and developments that can contribute to better understand the complexity of financial modelling and its ability to bridge financial theories and their practice. Future Perspectives in Risk Models and Finance begins with an extensive outline by Alain Bensoussan et al. of GLM estimation techniques combined with proofs of fundamental results. Applications to static and dynamic models provide a unified approach to the estimation of nonlinear risk models. A second section is concerned with the definition of risks and their management. In particular, Guegan and Hassani review a number of risk models definition emphasizing the importance of bi-modal distributions for financial regulation. An additional chapter provides a review of stress testing and their implications. Nassim Taleb and Sandis provide an anti-fragility approach based on “skin in the game”. To conclude, Raphael Douady discusses the noncyclical CAR (Capital Adequacy Rule) and their effects of aversion of systemic risks. A third section emphasizes analytic financial modelling approaches and techniques. Tapiero and Vallois provide an overview of mathematical systems and their use in financial modeling. These systems span the fundamental Arrow-Debreu framework underlying financial models of complete markets and subsequently, mathematical systems departing from this framework but yet generalizing their approach to dynamic financial models. Explicitly, models based on fractional calculus, on persistence (short memory) and on entropy-based non-extensiveness. Applications of these models are used to define a modeling approach to incomplete financial models and their potential use as a “measure of incompleteness”. Subsequently Bianchi and Pianese provide an extensive overview of multi-fractional models and their important applications to Asset price modeling. Finally, Tapiero and Jinquyi consider the binomial pricing model by discussing the effects of memory on the pricing of asset prices.

Natural Disasters, When Will They Reach Me?

Author : Isuri Wijesundera
Publisher : Springer
ISBN 13 : 9811011133
Total Pages : 128 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Natural Disasters, When Will They Reach Me? by : Isuri Wijesundera

Download or read book Natural Disasters, When Will They Reach Me? written by Isuri Wijesundera and published by Springer. This book was released on 2016-05-16 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expected time of impact, also known as the mean first passage time (MFPT) to reach failure, is a critical metric in the management of natural disasters. The complexity of the dynamics governing natural disasters lead to stochastic behaviour. This book shows that state transitions of many such systems translate into random walks on their respective state spaces, biased and shaped by environmental inhomogeneity. Thus the probabilistic treatment of those random walks gives valuable insights of expected behaviour. A comprehensive case study of predicting cyclone induced flood is followed by a discussion of generic methods that predict MFPT addressing directional bias. This is followed by discussing MFPT prediction methods in systems showing network inhomogeneity. All presented methods are illustrated using real datasets of natural disasters. The book ends with a short discussion of possible future research areas introducing the problem of predicting MFPT for bush-fire propagation.

Branching Random Walks

Author : Zhan Shi
Publisher : Springer
ISBN 13 : 3319253727
Total Pages : 133 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Branching Random Walks by : Zhan Shi

Download or read book Branching Random Walks written by Zhan Shi and published by Springer. This book was released on 2016-02-04 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time. Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.

Random Walks and Electric Networks

Author : Peter G. Doyle
Publisher : American Mathematical Soc.
ISBN 13 : 1614440220
Total Pages : 159 pages
Book Rating : 4.6/5 (144 download)

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Book Synopsis Random Walks and Electric Networks by : Peter G. Doyle

Download or read book Random Walks and Electric Networks written by Peter G. Doyle and published by American Mathematical Soc.. This book was released on 1984-12-31 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.

Random Walk, Brownian Motion, and Martingales

Author : Rabi Bhattacharya
Publisher : Springer Nature
ISBN 13 : 303078939X
Total Pages : 396 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Random Walk, Brownian Motion, and Martingales by : Rabi Bhattacharya

Download or read book Random Walk, Brownian Motion, and Martingales written by Rabi Bhattacharya and published by Springer Nature. This book was released on 2021-09-20 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov–Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.

Intersections of Random Walks

Author : Gregory F. Lawler
Publisher : Springer Science & Business Media
ISBN 13 : 1475721374
Total Pages : 219 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Intersections of Random Walks by : Gregory F. Lawler

Download or read book Intersections of Random Walks written by Gregory F. Lawler and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.

Random Walks and Diffusion

Author : Open University Course Team
Publisher :
ISBN 13 : 9780749251680
Total Pages : 200 pages
Book Rating : 4.2/5 (516 download)

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Book Synopsis Random Walks and Diffusion by : Open University Course Team

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.

Non-homogeneous Random Walks

Author : Mikhail Menshikov
Publisher : Cambridge University Press
ISBN 13 : 1316867366
Total Pages : 423 pages
Book Rating : 4.3/5 (168 download)

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Book Synopsis Non-homogeneous Random Walks by : Mikhail Menshikov

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.

Globalization, Gating, and Risk Finance

Author : Unurjargal Nyambuu
Publisher : John Wiley & Sons
ISBN 13 : 1119252709
Total Pages : 480 pages
Book Rating : 4.1/5 (192 download)

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Book Synopsis Globalization, Gating, and Risk Finance by : Unurjargal Nyambuu

Download or read book Globalization, Gating, and Risk Finance written by Unurjargal Nyambuu and published by John Wiley & Sons. This book was released on 2017-11-08 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth guide to global and risk finance based on financial models and data-based issues that confront global financial managers. Globalization, Gating, and Risk Finance offers perspectives on global risk finance in a world with economies in transition. Developed from lectures and research projects investigating the consequences of globalization and strategic approaches to fundamental economics and finance, it provides an approach based on financial models and data; it includes many case-study problems. The book departs from the traditional macroeconomic and financial approaches to global and strategic risk finance, where economic power and geopolitical issues are intermingled to create complex and forward-looking financial systems. Chapter coverage includes: Globalization: Economies in Collision; Data, Measurements, and Global Finance; Global Finance: Utility, Financial Consumption, and Asset Pricing; Macroeconomics, Foreign Exchange, and Global Finance; Foreign Exchange Models and Prices; Asia: Financial Environment and Risks; Financial Currency Pricing, Swaps, Derivatives, and Complete Markets; Credit Risk and International Debt; Globalization and Trade: A Changing World; and Compliance and Financial Regulation. Provides a framework for global financial and inclusive models, some of which are not commonly covered in other books. Considers risk management, utility, and utility-based multi-agent financial theories. Presents a theoretical framework to assist with a variety of problems ranging from derivatives and FX pricing to bond default to trade and strategic regulation. Provides detailed explanations and mathematical proofs to aid the readers’ understanding. Globalization, Gating, and Risk Finance is appropriate as a text for graduate students of global finance, general finance, financial engineering, and international economics, and for practitioners.