Aspects And Applications Of The Random Walk

Author : George Herbert Weiss
Publisher : Elsevier Science & Technology
Page : 388 pages
File Size : 53,7 Mb
Release : 1994
Category : Computers
ISBN : UOM:39015032947924

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Aspects and Applications of the Random Walk by George Herbert Weiss Pdf

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 : Joseph Rudnick,George Gaspari
Publisher : Cambridge University Press
Page : 348 pages
File Size : 40,8 Mb
Release : 2010-03-25
Category : Science
ISBN : 0521535832

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Elements of the Random Walk by Joseph Rudnick,George Gaspari Pdf

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.

Author : Michael F Shlesinger
Publisher : World Scientific
Page : 214 pages
File Size : 42,9 Mb
Release : 2021-06-29
Category : Mathematics
ISBN : 9789811232824

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An Unbounded Experience In Random Walks With Applications by Michael F Shlesinger Pdf

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.

Author : Michael N. Barber,B. W. Ninham
Publisher : CRC Press
Page : 190 pages
File Size : 55,8 Mb
Release : 1970
Category : Mathematics
ISBN : 067702620X

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Random and Restricted Walks by Michael N. Barber,B. W. Ninham Pdf

Author : Alain Bensoussan,Dominique Guegan,Charles S. Tapiero
Publisher : Springer
Page : 315 pages
File Size : 46,6 Mb
Release : 2014-11-20
Category : Business & Economics
ISBN : 9783319075242

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Future Perspectives in Risk Models and Finance by Alain Bensoussan,Dominique Guegan,Charles S. Tapiero Pdf

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.

Author : Isuri Wijesundera,Malka N. Halgamuge,Thrishantha Nanayakkara,Thas Nirmalathas
Publisher : Springer
Page : 128 pages
File Size : 51,6 Mb
Release : 2016-05-16
Category : Nature
ISBN : 9789811011139

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Natural Disasters, When Will They Reach Me? by Isuri Wijesundera,Malka N. Halgamuge,Thrishantha Nanayakkara,Thas Nirmalathas Pdf

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.

Author : Serguei Popov
Publisher : Cambridge University Press
Page : 224 pages
File Size : 41,9 Mb
Release : 2021-03-18
Category : Mathematics
ISBN : 9781108472456

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Two-Dimensional Random Walk by Serguei Popov Pdf

A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.

Author : Nadine Guillotin-Plantard,Rene Schott
Publisher : Elsevier
Page : 279 pages
File Size : 41,7 Mb
Release : 2006-02-08
Category : Mathematics
ISBN : 9780080462844

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Dynamic Random Walks by Nadine Guillotin-Plantard,Rene Schott Pdf

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

Author : Unurjargal Nyambuu,Charles S. Tapiero
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 41,6 Mb
Release : 2017-11-08
Category : Business & Economics
ISBN : 9781119252702

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Globalization, Gating, and Risk Finance by Unurjargal Nyambuu,Charles S. Tapiero Pdf

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.

Author : Bruce J. West,Paolo Grigolini
Publisher : Cambridge University Press
Page : 386 pages
File Size : 54,7 Mb
Release : 2010-12-23
Category : Technology & Engineering
ISBN : 9781139493772

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Complex Webs by Bruce J. West,Paolo Grigolini Pdf

Complex Webs synthesises modern mathematical developments with a broad range of complex network applications of interest to the engineer and system scientist, presenting the common principles, algorithms, and tools governing network behaviour, dynamics, and complexity. The authors investigate multiple mathematical approaches to inverse power laws and expose the myth of normal statistics to describe natural and man-made networks. Richly illustrated throughout with real-world examples including cell phone use, accessing the Internet, failure of power grids, measures of health and disease, distribution of wealth, and many other familiar phenomena from physiology, bioengineering, biophysics, and informational and social networks, this book makes thought-provoking reading. With explanations of phenomena, diagrams, end-of-chapter problems, and worked examples, it is ideal for advanced undergraduate and graduate students in engineering and the life, social, and physical sciences. It is also a perfect introduction for researchers who are interested in this exciting new way of viewing dynamic networks.

Author : Heinz Georg Schuster
Publisher : John Wiley & Sons
Page : 260 pages
File Size : 55,9 Mb
Release : 2010-07-06
Category : Science
ISBN : 352763097X

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Reviews of Nonlinear Dynamics and Complexity by Heinz Georg Schuster Pdf

Written in a style that breaks the barriers between the disciplines, this monograph enables researchers from life science, physics, engineering, or chemistry to access the most recent results in a common language. The resulting review character of this project sets it apart from specialized journals, and allows each volume to respond quickly to new developments. This third volume contains new topics ranging from chaotic computing, via random dice tossing and stochastic limit-cycle oscillators, to a number theoretic example of self-organized criticality, wave localization in complex networks and anomalous diffusion. A first-class board of international scientists advises the editor, such that the carefully selected and invited contributions represent the latest and most relevant findings.

Author : V. Balakrishnan
Publisher : Springer Nature
Page : 314 pages
File Size : 50,8 Mb
Release : 2020-12-04
Category : Science
ISBN : 9783030622336

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Elements of Nonequilibrium Statistical Mechanics by V. Balakrishnan Pdf

This book deals with the basic principles and techniques of nonequilibrium statistical mechanics. The importance of this subject is growing rapidly in view of the advances being made, both experimentally and theoretically, in statistical physics, chemical physics, biological physics, complex systems and several other areas. The presentation of topics is quite self-contained, and the choice of topics enables the student to form a coherent picture of the subject. The approach is unique in that classical mechanical formulation takes center stage. The book is of particular interest to advanced undergraduate and graduate students in engineering departments.

Author : Charles S. Tapiero
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 40,8 Mb
Release : 2013-02-13
Category : Business & Economics
ISBN : 9781461462347

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Engineering Risk and Finance by Charles S. Tapiero Pdf

Risk models are models of uncertainty, engineered for some purposes. They are “educated guesses and hypotheses” assessed and valued in terms of well-defined future states and their consequences. They are engineered to predict, to manage countable and accountable futures and to provide a frame of reference within which we may believe that “uncertainty is tamed”. Quantitative-statistical tools are used to reconcile our information, experience and other knowledge with hypotheses that both serve as the foundation of risk models and also value and price risk. Risk models are therefore common to most professions, each with its own methods and techniques based on their needs, experience and a wisdom accrued over long periods of time. This book provides a broad and interdisciplinary foundation to engineering risks and to their financial valuation and pricing. Risk models applied in industry and business, heath care, safety, the environment and regulation are used to highlight their variety while financial valuation techniques are used to assess their financial consequences. This book is technically accessible to all readers and students with a basic background in probability and statistics (with 3 chapters devoted to introduce their elements). Principles of risk measurement, valuation and financial pricing as well as the economics of uncertainty are outlined in 5 chapters with numerous examples and applications. New results, extending classical models such as the CCAPM are presented providing insights to assess the risks and their price in an interconnected, dependent and strategic economic environment. In an environment departing from the fundamental assumptions we make regarding financial markets, the book provides a strategic/game-like approach to assess the risk and the opportunities that such an environment implies. To control these risks, a strategic-control approach is developed that recognizes that many risks resulting by “what we do” as well as “what others do”. In particular we address the strategic and statistical control of compliance in large financial institutions confronted increasingly with a complex and far more extensive regulation.

Author : Allan Gut
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 53,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475719925

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Stopped Random Walks by Allan Gut Pdf

My first encounter with renewal theory and its extensions was in 1967/68 when I took a course in probability theory and stochastic processes, where the then recent book Stochastic Processes by Professor N.D. Prabhu was one of the requirements. Later, my teacher, Professor Carl-Gustav Esseen, gave me some problems in this area for a possible thesis, the result of which was Gut (1974a). Over the years I have, on and off, continued research in this field. During this time it has become clear that many limit theorems can be obtained with the aid of limit theorems for random walks indexed by families of positive, integer valued random variables, typically by families of stopping times. During the spring semester of 1984 Professor Prabhu visited Uppsala and very soon got me started on a book focusing on this aspect. I wish to thank him for getting me into this project, for his advice and suggestions, as well as his kindness and hospitality during my stay at Cornell in the spring of 1985. Throughout the writing of this book I have had immense help and support from Svante Janson. He has not only read, but scrutinized, every word and every formula of this and earlier versions of the manuscript. My gratitude to him for all the errors he found, for his perspicacious suggestions and remarks and, above all, for what his unusual personal as well as scientific generosity has meant to me cannot be expressed in words.

Author : J. Klafter,I. M. Sokolov
Publisher : Oxford University Press
Page : 161 pages
File Size : 46,9 Mb
Release : 2011-08-18
Category : Business & Economics
ISBN : 9780199234868

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First Steps in Random Walks by J. Klafter,I. M. Sokolov Pdf

Random walks proved to be a useful model of many complex transport processes at the micro and macroscopical level in physics and chemistry, economics, biology and other disciplines. The book discusses the main variants of random walks and gives the most important mathematical tools for their theoretical description.