Principles Of Random Walk Zz

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Principles of Random Walk. (ZZ)

Author : Frank Spitzer
Publisher : Methuen Paperback
ISBN 13 : 9781475742312
Total Pages : 0 pages
Book Rating : 4.7/5 (423 download)

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Book Synopsis Principles of Random Walk. (ZZ) by : Frank Spitzer

Download or read book Principles of Random Walk. (ZZ) written by Frank Spitzer and published by Methuen Paperback. This book was released on 2022-12-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Principles of Random Walk

Author : Frank Spitzer
Publisher : Springer Science & Business Media
ISBN 13 : 1475742290
Total Pages : 419 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Principles of Random Walk by : Frank Spitzer

Download or read book Principles of Random Walk written by Frank Spitzer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Potential Functions of Random Walks in Z with Infinite Variance

Author : Kôhei Uchiyama
Publisher : Springer Nature
ISBN 13 : 3031410203
Total Pages : 277 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Potential Functions of Random Walks in Z with Infinite Variance by : Kôhei Uchiyama

Download or read book Potential Functions of Random Walks in Z with Infinite Variance written by Kôhei Uchiyama and published by Springer Nature. This book was released on 2023 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the potential functions of one-dimensional recurrent random walks on the lattice of integers with step distribution of infinite variance. The central focus is on obtaining reasonably nice estimates of the potential function. These estimates are then applied to various situations, yielding precise asymptotic results on, among other things, hitting probabilities of finite sets, overshoot distributions, Green functions on long finite intervals and the half-line, and absorption probabilities of two-sided exit problems. The potential function of a random walk is a central object in fluctuation theory. If the variance of the step distribution is finite, the potential function has a simple asymptotic form, which enables the theory of recurrent random walks to be described in a unified way with rather explicit formulae. On the other hand, if the variance is infinite, the potential function behaves in a wide range of ways depending on the step distribution, which the asymptotic behaviour of many functionals of the random walk closely reflects. In the case when the step distribution is attracted to a strictly stable law, aspects of the random walk have been intensively studied and remarkable results have been established by many authors. However, these results generally do not involve the potential function, and important questions still need to be answered. In the case where the random walk is relatively stable, or if one tail of the step distribution is negligible in comparison to the other on average, there has been much less work. Some of these unsettled problems have scarcely been addressed in the last half-century. As revealed in this treatise, the potential function often turns out to play a significant role in their resolution. Aimed at advanced graduate students specialising in probability theory, this book will also be of interest to researchers and engineers working with random walks and stochastic systems.

Principles of Random Walk

Author : Frank Ludvig Spitzer
Publisher :
ISBN 13 : 9787506200646
Total Pages : 408 pages
Book Rating : 4.2/5 (6 download)

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Book Synopsis Principles of Random Walk by : Frank Ludvig Spitzer

Download or read book Principles of Random Walk written by Frank Ludvig Spitzer and published by . This book was released on 1976 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Statistical Mechanics and Random Walks

Author : Abram Skogseid
Publisher :
ISBN 13 : 9781614709664
Total Pages : 0 pages
Book Rating : 4.7/5 (96 download)

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Book Synopsis Statistical Mechanics and Random Walks by : Abram Skogseid

Download or read book Statistical Mechanics and Random Walks written by Abram Skogseid and published by . This book was released on 2011-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Markov Chains and Mixing Times

Author : David Asher Levin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886274
Total Pages : 396 pages
Book Rating : 4.8/5 (862 download)

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Book Synopsis Markov Chains and Mixing Times by : David Asher Levin

Download or read book Markov Chains and Mixing Times written by David Asher Levin and published by American Mathematical Soc.. This book was released on with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. Markov Chains and Mixing Times is meant to bring the excitement of this active area of research to a wide audience.

Random Walk in Random and Non-random Environments

Author : P l Rvsz
Publisher : World Scientific
ISBN 13 : 9812703365
Total Pages : 400 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Random Walk in Random and Non-random Environments by : P l Rvsz

Download or read book Random Walk in Random and Non-random Environments written by P l Rvsz and published by World Scientific. This book was released on 2005 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results OCo mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk. Since the first edition was published in 1990, a number of new results have appeared in the literature. The original edition contained many unsolved problems and conjectures which have since been settled; this second revised and enlarged edition includes those new results. Three new chapters have been added: frequently and rarely visited points, heavy points and long excursions. This new edition presents the most complete study of, and the most elementary way to study, the path properties of the Brownian motion."

Random Walks, Brownian Motion, and Interacting Particle Systems

Author : H. Kesten
Publisher : Springer Science & Business Media
ISBN 13 : 1461204593
Total Pages : 457 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Random Walks, Brownian Motion, and Interacting Particle Systems by : H. Kesten

Download or read book Random Walks, Brownian Motion, and Interacting Particle Systems written by H. Kesten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. The last area was started by Frank as part of the general resurgence of treating problems of statistical mechanics with rigorous probabilistic tools.

Markov Chains and Mixing Times: Second Edition

Author : David A. Levin
Publisher : American Mathematical Soc.
ISBN 13 : 1470429624
Total Pages : 447 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Markov Chains and Mixing Times: Second Edition by : David A. Levin

Download or read book Markov Chains and Mixing Times: Second Edition written by David A. Levin and published by American Mathematical Soc.. This book was released on 2017-10-31 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines. The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times. The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.

Two-Dimensional Random Walk

Author : Serguei Popov
Publisher : Cambridge University Press
ISBN 13 : 1108591124
Total Pages : 225 pages
Book Rating : 4.1/5 (85 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 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at the active edge of research. It starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. After reviewing some relevant potential-theoretic tools, the reader is guided toward the relatively new topic of random interlacements - which can be viewed as a 'canonical soup' of nearest-neighbour loops through infinity - again with emphasis on two dimensions. On the way, readers will visit conditioned simple random walks - which are the 'noodles' in the soup - and also discover how Poisson processes of infinite objects are constructed and review the recently introduced method of soft local times. Each chapter ends with many exercises, making it suitable for courses and independent study.

Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups

Author : Zhen-Qing Chen
Publisher : Springer Nature
ISBN 13 : 3031433327
Total Pages : 147 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups by : Zhen-Qing Chen

Download or read book Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups written by Zhen-Qing Chen and published by Springer Nature. This book was released on 2023-11-25 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits in these limit theorems are Lévy processes on some simply connected nilpotent Lie groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit Lévy processes in the context of (non-commutative) nilpotent groups.

Theory of Probability and Random Processes

Author : Leonid Koralov
Publisher : Springer Science & Business Media
ISBN 13 : 3540688293
Total Pages : 346 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Theory of Probability and Random Processes by : Leonid Koralov

Download or read book Theory of Probability and Random Processes written by Leonid Koralov and published by Springer Science & Business Media. This book was released on 2007-08-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion.

Random Walk In Random And Non-random Environments (Third Edition)

Author : Revesz Pal
Publisher : World Scientific
ISBN 13 : 9814447528
Total Pages : 420 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Random Walk In Random And Non-random Environments (Third Edition) by : Revesz Pal

Download or read book Random Walk In Random And Non-random Environments (Third Edition) written by Revesz Pal and published by World Scientific. This book was released on 2013-03-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results — mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. Some of the obtained results are also presented.

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.

Limit Theorems for Functionals of Random Walks

Author : A. N. Borodin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821804384
Total Pages : 276 pages
Book Rating : 4.8/5 (43 download)

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Book Synopsis Limit Theorems for Functionals of Random Walks by : A. N. Borodin

Download or read book Limit Theorems for Functionals of Random Walks written by A. N. Borodin and published by American Mathematical Soc.. This book was released on 1995 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines traditional problems in the theory of random walks: limit theorems for additive and multiadditive functionals defined on a random walk. Although the problems are traditional, the methods presented here are new. The book is intended for experts in probability theory and its applications, as well as for undergraduate and graduate students specializing in these areas.

Random Walks on Disordered Media and their Scaling Limits

Author : Takashi Kumagai
Publisher : Springer
ISBN 13 : 331903152X
Total Pages : 147 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Random Walks on Disordered Media and their Scaling Limits by : Takashi Kumagai

Download or read book Random Walks on Disordered Media and their Scaling Limits written by Takashi Kumagai and published by Springer. This book was released on 2014-01-25 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster(‘the ant in the labyrinth’)is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.