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.
Author: Frank Spitzer
Publisher: Springer Science & Business Media
ISBN: 9780387951546
Category : Mathematics
Languages : en
Pages : 438
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Book Description
More than 100 pages of examples and problems illustrate and clarify the presentation."--BOOK JACKET.
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.
Author: Aleksandr Alekseevich Borovkov
Publisher: Cambridge University Press
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 655
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Book Description
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.
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.
Author: Burton G. Malkiel
Publisher: W. W. Norton & Company
ISBN: 0393330338
Category : Business & Economics
Languages : en
Pages : 454
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Book Description
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.
Author: Burton Gordon Malkiel
Publisher: W. W. Norton & Company
ISBN: 9780393057829
Category : Business & Economics
Languages : en
Pages : 422
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Book Description
An informative guide to successful investing, offering a vast array of advice on how investors can tilt the odds in their favour.
Author: Howard C. Berg
Publisher: Princeton University Press
ISBN: 1400820022
Category : Science
Languages : en
Pages : 166
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Book Description
This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.
Author: R.L. Weber
Publisher: CRC Press
ISBN: 9780854980406
Category : Science
Languages : en
Pages : 236
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Book Description
More Random Walks in Science is an anthology of fascinating and frequently amusing anecdotes, quotations, illustrations, articles, and reviews that reflect the more lighthearted aspects of the scientific world and the less serious excursions of the scientific mind. The book is guaranteed to delight anyone who has a professional or amateur interest in science.
Author: Wolfgang König
Publisher: Birkhäuser
ISBN: 3319335960
Category : Mathematics
Languages : en
Pages : 199
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Book Description
This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
