Random Walk A Modern Introduction

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Random Walk: A Modern Introduction

Gregory F. Lawler,Vlada Limic
Random Walk A Modern Introduction Book PDF

Author : Gregory F. Lawler,Vlada Limic
Publisher : Cambridge University Press
Page : 377 pages
File Size : 52,9 Mb
Release : 2010-06-24
Category : Mathematics
ISBN : 9781139488761

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Random Walk: A Modern Introduction by Gregory F. Lawler,Vlada Limic Pdf

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.

Random Walk

Gregory F. Lawler,Vlada Limic
Random Walk Book PDF

Author : Gregory F. Lawler,Vlada Limic
Publisher : Unknown
Page : 378 pages
File Size : 55,7 Mb
Release : 2014-05-14
Category : Mathematics
ISBN : 0511750110

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Random Walk by Gregory F. Lawler,Vlada Limic Pdf

An advanced treatment of random walks written for students and researchers in probability and related fields.

Random Walks on Reductive Groups

Yves Benoist,Jean-François Quint
Random Walks on Reductive Groups Book PDF

Author : Yves Benoist,Jean-François Quint
Publisher : Springer
Page : 323 pages
File Size : 41,9 Mb
Release : 2016-10-20
Category : Mathematics
ISBN : 9783319477213

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Random Walks on Reductive Groups by Yves Benoist,Jean-François Quint Pdf

The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.

Random Walk and the Heat Equation

Gregory F. Lawler
Random Walk and the Heat Equation Book PDF

Author : Gregory F. Lawler
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 52,6 Mb
Release : 2010-11-22
Category : Mathematics
ISBN : 9780821848296

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Random Walk and the Heat Equation by Gregory F. Lawler Pdf

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.

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

Burton G. Malkiel
A Random Walk Down Wall Street The Time Tested Strategy for Successful Investing Ninth Edition Book PDF

Author : Burton G. Malkiel
Publisher : W. W. Norton & Company
Page : 454 pages
File Size : 50,6 Mb
Release : 2007-12-17
Category : Business & Economics
ISBN : 9780393330335

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

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.

Intersections of Random Walks

Gregory F. Lawler
Intersections of Random Walks Book PDF

Author : Gregory F. Lawler
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 53,7 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 9781461459729

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Intersections of Random Walks by Gregory F. Lawler Pdf

A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry. Originally published in 1991, Intersections of Random Walks focuses on and explores a number of problems dealing primarily with the nonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical phenomena. Topics include: discrete harmonic measure, including an introduction to diffusion limited aggregation (DLA); the probability that independent random walks do not intersect; and properties of walks without self-intersections. The present softcover reprint includes corrections and addenda from the 1996 printing, and makes this classic monograph available to a wider audience. With a self-contained introduction to the properties of simple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic properties of random walks.

Two-Dimensional Random Walk

Serguei Popov
Two Dimensional Random Walk Book PDF

Author : Serguei Popov
Publisher : Cambridge University Press
Page : 224 pages
File Size : 54,6 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.

Elements of Random Walk and Diffusion Processes

Oliver C. Ibe
Elements of Random Walk and Diffusion Processes Book PDF

Author : Oliver C. Ibe
Publisher : John Wiley & Sons
Page : 280 pages
File Size : 54,7 Mb
Release : 2013-09-23
Category : Mathematics
ISBN : 9781118618097

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Elements of Random Walk and Diffusion Processes by Oliver C. Ibe Pdf

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.

A Modern Introduction to Probability and Statistics

F.M. Dekking,C. Kraaikamp,H.P. Lopuhaä,L.E. Meester
A Modern Introduction to Probability and Statistics Book PDF

Author : F.M. Dekking,C. Kraaikamp,H.P. Lopuhaä,L.E. Meester
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 46,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9781846281686

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A Modern Introduction to Probability and Statistics by F.M. Dekking,C. Kraaikamp,H.P. Lopuhaä,L.E. Meester Pdf

Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

A Non-Random Walk Down Wall Street

Andrew W. Lo,A. Craig MacKinlay
A Non Random Walk Down Wall Street Book PDF

Author : Andrew W. Lo,A. Craig MacKinlay
Publisher : Princeton University Press
Page : 449 pages
File Size : 44,8 Mb
Release : 2011-11-14
Category : Business & Economics
ISBN : 9781400829095

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A Non-Random Walk Down Wall Street by Andrew W. Lo,A. Craig MacKinlay Pdf

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.

Random Walk, Brownian Motion, and Martingales

Rabi Bhattacharya,Edward C. Waymire
Random Walk Brownian Motion and Martingales Book PDF

Author : Rabi Bhattacharya,Edward C. Waymire
Publisher : Springer Nature
Page : 396 pages
File Size : 48,9 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9783030789398

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Random Walk, Brownian Motion, and Martingales by Rabi Bhattacharya,Edward C. Waymire Pdf

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.

Global Finance And Financial Markets: A Modern Introduction

Ferdinand E Banks
Global Finance And Financial Markets A Modern Introduction Book PDF

Author : Ferdinand E Banks
Publisher : World Scientific Publishing Company
Page : 333 pages
File Size : 52,6 Mb
Release : 2001-02-19
Category : Business & Economics
ISBN : 9789813102743

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Global Finance And Financial Markets: A Modern Introduction by Ferdinand E Banks Pdf

This is an elementary, up-to-date text and reference book in global finance. It has been especially designed for beginning students in economics and finance, and also for self-study by anyone with a knowledge of secondary school algebra and an interest in finance and financial markets. The subjects taken up in some details are stocks (shares), bonds, interest rates and derivatives, particularly futures, options, and swaps. There are also chapters on exchange rates and banking, and readers are provided with an elementary introduction to risk and uncertainty. The book is also an easily read supplement to more technical presentations, in that it introduces all categories of readers to real world financial markets.

A Lifetime of Excursions Through Random Walks and Lévy Processes

Loïc Chaumont,Andreas E. Kyprianou
A Lifetime of Excursions Through Random Walks and L vy Processes Book PDF

Author : Loïc Chaumont,Andreas E. Kyprianou
Publisher : Springer Nature
Page : 354 pages
File Size : 50,6 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030833091

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A Lifetime of Excursions Through Random Walks and Lévy Processes by Loïc Chaumont,Andreas E. Kyprianou Pdf

This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.

Non-homogeneous Random Walks

Mikhail Menshikov,Serguei Popov,Andrew Wade
Non homogeneous Random Walks Book PDF

Author : Mikhail Menshikov,Serguei Popov,Andrew Wade
Publisher : Cambridge University Press
Page : 423 pages
File Size : 43,8 Mb
Release : 2016-12-22
Category : Mathematics
ISBN : 9781316867365

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Non-homogeneous Random Walks by Mikhail Menshikov,Serguei Popov,Andrew Wade Pdf

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.

Random Walks and Heat Kernels on Graphs

M. T. Barlow
Random Walks and Heat Kernels on Graphs Book PDF

Author : M. T. Barlow
Publisher : Cambridge University Press
Page : 239 pages
File Size : 51,7 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9781107674424

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Random Walks and Heat Kernels on Graphs by M. T. Barlow Pdf

Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.