Principles of Random Walk

Principles of Random Walk

Author: Frank Spitzer

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 419

ISBN-13: 1475742290

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This book is devoted exclusively to a very special class of random processes, namely, to random walk on the lattice points of ordinary Euclidian space. The author considers this high degree of specialization worthwhile because the theory of such random walks is far more complete than that of any larger class of Markov chains. Almost 100 pages of examples and problems are included.


Principles of Random Walk

Principles of Random Walk

Author: Frank Spitzer

Publisher: Springer Science & Business Media

Published: 2001

Total Pages: 438

ISBN-13: 9780387951546

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More than 100 pages of examples and problems illustrate and clarify the presentation."--BOOK JACKET.


Random Walk and the Heat Equation

Random Walk and the Heat Equation

Author: Gregory F. Lawler

Publisher: American Mathematical Soc.

Published: 2010-11-22

Total Pages: 170

ISBN-13: 0821848291

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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.


asymptotic analysis of random walks

asymptotic analysis of random walks

Author: Aleksandr Alekseevich Borovkov

Publisher: Cambridge University Press

Published: 2008

Total Pages: 655

ISBN-13:

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A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.


Statistical Mechanics and Random Walks

Statistical Mechanics and Random Walks

Author: Abram Skogseid

Publisher:

Published: 2011-10

Total Pages: 0

ISBN-13: 9781614709664

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In this book, the authors gather and present topical research in the study of statistical mechanics and random walk principles and applications. Topics discussed in this compilation include the application of stochastic approaches to modelling suspension flow in porous media; subordinated Gaussian processes; random walk models in biophysical science; non-equilibrium dynamics and diffusion processes; global random walk algorithm for diffusion processes and application of random walks for the analysis of graphs, musical composition and language phylogeny.


A Random Walk Down Wall Street

A Random Walk Down Wall Street

Author: Burton Gordon Malkiel

Publisher: W. W. Norton & Company

Published: 2003

Total Pages: 422

ISBN-13: 9780393057829

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An informative guide to successful investing, offering a vast array of advice on how investors can tilt the odds in their favour.


A Random Walk in Physics

A Random Walk in Physics

Author: Massimo Cencini

Publisher: Springer Nature

Published: 2021-06-15

Total Pages: 220

ISBN-13: 3030725316

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This book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book features 28 key entries and it is carefully structured so as to allow readers to pursue different paths that reflect their interests and priorities, thereby avoiding an excessively systematic presentation that might stifle interest. While the majority of the entries concern specific topics and arguments, some relate to important protagonists of science, highlighting and explaining their contributions. Advanced mathematics is avoided, and formulas are introduced in only a few cases. The book is a user-friendly tool that nevertheless avoids scientific compromise. It is of interest to all who seek a better grasp of the world that surrounds us and of the ideas that have changed our perceptions.


A Non-Random Walk Down Wall Street

A Non-Random Walk Down Wall Street

Author: Andrew W. Lo

Publisher: Princeton University Press

Published: 2011-11-14

Total Pages: 449

ISBN-13: 1400829097

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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.


Random Walks and Heat Kernels on Graphs

Random Walks and Heat Kernels on Graphs

Author: M. T. Barlow

Publisher: Cambridge University Press

Published: 2017-02-23

Total Pages: 239

ISBN-13: 1107674425

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