Principles of Random Walk

Principles of Random Walk PDF Author: Frank Spitzer
Publisher: Springer Science & Business Media
ISBN: 1475742290
Category : Mathematics
Languages : en
Pages : 419

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Book Description
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 PDF Author: Frank Spitzer
Publisher: Springer Science & Business Media
ISBN: 1475742290
Category : Mathematics
Languages : en
Pages : 419

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Book Description
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.

Random Walk and the Heat Equation

Random Walk and the Heat Equation PDF Author: Gregory F. Lawler
Publisher: American Mathematical Soc.
ISBN: 0821848291
Category : Mathematics
Languages : en
Pages : 170

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Book Description
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.

Two-Dimensional Random Walk

Two-Dimensional Random Walk PDF Author: Serguei Popov
Publisher: Cambridge University Press
ISBN: 1108472451
Category : Mathematics
Languages : en
Pages : 224

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

Principles of Random Walk

Principles of Random Walk PDF Author: Frank Ludvig Spitzer
Publisher:
ISBN: 9787506200646
Category : Random walks (Mathematics)
Languages : en
Pages : 408

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Book Description


Asymptotic Analysis of Random Walks

Asymptotic Analysis of Random Walks PDF Author: K A Borovkov
Publisher:
ISBN: 9781299909281
Category :
Languages : en
Pages :

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Book Description
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 PDF Author: Abram Skogseid
Publisher:
ISBN: 9781614709664
Category : Engineering mathematics
Languages : en
Pages : 0

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Book Description
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.

Principles of Random Walk. (ZZ)

Principles of Random Walk. (ZZ) PDF Author: Frank Spitzer
Publisher: Methuen Paperback
ISBN: 9781475742312
Category : Mathematics
Languages : en
Pages : 0

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Book Description
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.

Intersections of Random Walks

Intersections of Random Walks PDF Author: Gregory F. Lawler
Publisher: Springer Science & Business Media
ISBN: 1475721374
Category : Mathematics
Languages : en
Pages : 219

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Book Description
A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.

Principles of Random Walk

Principles of Random Walk PDF Author: F. Spitzer
Publisher: Springer
ISBN: 9781468462579
Category : Mathematics
Languages : en
Pages : 0

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Book Description
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.

Random Walk: A Modern Introduction

Random Walk: A Modern Introduction PDF Author: Gregory F. Lawler
Publisher: Cambridge University Press
ISBN: 1139488767
Category : Mathematics
Languages : en
Pages : 377

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Book Description
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.