Principles Of Random Walk
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Principles Of Random Walk
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Author : Frank Spitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Principles Of Random Walk written by Frank Spitzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
More than 100 pages of examples and problems illustrate and clarify the presentation."--BOOK JACKET.
Principles Of Random Walk
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Author : Frank Ludvig Spitzer
language : en
Publisher:
Release Date : 1976
Principles Of Random Walk written by Frank Ludvig Spitzer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Random walks (Mathematics) categories.
Principles Of Random Walk
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Author : Frank Spitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Principles Of Random Walk written by Frank Spitzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
In this edition a large number of errors have been corrected, an occasional proof has been streamlined, and a number of references are made to recent pro gress. These references are to a supplementary bibliography, whose items are referred to as [S1] through [S26]. A thorough revision was not attempted. The development of the subject in the last decade would have required a treatment in a much more general con text. It is true that a number of interesting questions remain open in the concrete setting of random walk on the integers. (See [S 19] for a recent survey). On the other hand, much of the material of this book (foundations, fluctuation theory, renewal theorems) is now available in standard texts, e.g. Feller [S9], Breiman [S1], Chung [S4] in the more general setting of random walk on the real line. But the major new development since the first edition occurred in 1969, when D. Ornstein [S22] and C. J. Stone [S26] succeeded in extending the recurrent potential theory in· Chapters II and VII from the integers to the reals. By now there is an extensive and nearly complete potential theory of recurrent random walk on locally compact groups, Abelian ( [S20], [S25]) as well as non Abelian ( [S17], [S2] ). Finally, for the non-specialist there exists now an unsurpassed brief introduction to probabilistic potential theory, in the context of simple random walk and Brownian motion, by Dynkin and Yushkevich [S8].
Principles Of Random Walk Zz
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Author : Frank Spitzer
language : en
Publisher: Methuen Paperback
Release Date : 2022-12-22
Principles Of Random Walk Zz written by Frank Spitzer and has been published by Methuen Paperback this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-22 with Mathematics categories.
This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. The author considered this high degree of specialization worth while, because of the theory of such random walks is far more complete than that of any larger class of Markov chains. The book will present no technical difficulties to the readers with some solid experience in analysis in two or three of the following areas: probability theory, real variables and measure, analytic functions, Fourier analysis, differential and integral operators. There are almost 100 pages of examples and problems.
Asymptotic Analysis Of Random Walks
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Author : Aleksandr Alekseevich Borovkov
language : en
Publisher: Cambridge University Press
Release Date : 2008
Asymptotic Analysis Of Random Walks written by Aleksandr Alekseevich Borovkov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Asymptotic expansions categories.
This monograph is devoted to studying the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks, with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. It presents a unified and systematic exposition.
Principles Of Random Walk
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Author : F. Spitzer
language : en
Publisher: Springer
Release Date : 1976
Principles Of Random Walk written by F. Spitzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. I considered this high degree of specialization worth while, because the theory of such random walks is far more complete than that of any larger class of Markov chains. Random walk occupies such a privileged position primarily because of a delicate interplay between methods from harmonic analysis on one hand, and from potential theory on the other. The relevance of harmonic analysis to random walk of course stems from the invariance of the transition probabilities under translation in the additive group which forms the state space. It is precisely for this reason that, until recently, the subject was dominated by the analysis of characteristic functions (Fourier transforms of the transition probabilities). But if harmonic analysis were the central theme of this book, then the restriction to random walk on the integers (rather than on the reals, or on o'ther Abelian groups) would be quite unforgivable. Indeed it was the need for a self contained elementary exposition of the connection of harmonic analysis with the much more recent developments in potential theory that dictated the simplest possible setting.
Statistical Mechanics And Random Walks
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Author : Abram Skogseid
language : en
Publisher:
Release Date : 2011-10
Statistical Mechanics And Random Walks written by Abram Skogseid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10 with Engineering mathematics categories.
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.
Random Walk And The Heat Equation
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Author : Gregory F. Lawler
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-11-22
Random Walk And The Heat Equation written by Gregory F. Lawler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-22 with Mathematics categories.
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.
Random Walk Brownian Motion And Martingales
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Author : Rabi Bhattacharya
language : en
Publisher: Springer Nature
Release Date : 2021-09-20
Random Walk Brownian Motion And Martingales written by Rabi Bhattacharya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Mathematics categories.
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.
A Random Walk Down Wall Street The Time Tested Strategy For Successful Investing Ninth Edition
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Author : Burton G. Malkiel
language : en
Publisher: W. W. Norton & Company
Release Date : 2007-12-17
A Random Walk Down Wall Street The Time Tested Strategy For Successful Investing Ninth Edition written by Burton G. Malkiel and has been published by W. W. Norton & Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-17 with Business & Economics categories.
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.