Asymptotic Analysis of Random Walks

Author: A. A. Borovkov
Publisher: Cambridge University Press
ISBN:
Format: PDF, ePub, Docs
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A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.

Irrfahrten und verwandte Zuf lle

Author: Norbert Henze
Publisher: Springer-Verlag
ISBN: 3658018518
Format: PDF, Mobi
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Dem Autor des bekannten Lehrwerkes "Stochastik für Einsteiger" gelingt mit diesem Buch auf geradezu spielerische Weise, den Leser mit zahlreichen überraschenden Zufallsphänomenen und Nicht-Standard-Grenzwertsätzen im Zusammenhang mit einfachen Irrfahrten und verwandten Themen zu fesseln. Das Werk besticht mit einer durchgängig problemorientierten, lebendigen Darstellung, zu der auch fast 100 anschauliche Bilder beitragen. Es wird immer wieder konkret Modellbildung betrieben, und die erhaltenen Ergebnisse werden ausführlich diskutiert und vernetzt. Studierende, die dieses Werk in Proseminaren zur Stochastik getestet haben, waren insbesondere vom Zusammenspiel von geometrischen Argumenten (Spiegelungsprinzip), Kombinatorik, elementarer Stochastik und Analysis fasziniert. ​

Stochastic Simulation Algorithms and Analysis

Author: Søren Asmussen
Publisher: Springer Science & Business Media
ISBN: 0387690336
Format: PDF
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Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods; the second half discusses model-specific algorithms. Exercises and illustrations are included.

Random Walks and Heat Kernels on Graphs

Author: Martin T. Barlow
Publisher: Cambridge University Press
ISBN: 1107674425
Format: PDF
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This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincar inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.

Regular Variation

Author: N. H. Bingham
Publisher: Cambridge University Press
ISBN: 9780521379434
Format: PDF, Mobi
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A comprehensive account of the theory and applications of regular variation.

The Novikov Conjecture

Author: Matthias Kreck
Publisher: Springer Science & Business Media
ISBN: 9783764373153
Format: PDF
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These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.

Refined Large Deviation Limit Theorems

Author: Vladimir Vinogradov
Publisher: CRC Press
ISBN: 9780582254992
Format: PDF, Mobi
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This is a developing area of modern probability theory, which has applications in many areas. This volume is devoted to the systematic study of results on large deviations in situations where Cramér's condition on the finiteness of exponential moments may not be satisfied

Large random matrices

Author: Alice Guionnet
Publisher: Springer Science & Business Media
ISBN: 3540698965
Format: PDF, ePub, Mobi
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These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.

An Invitation to Modern Number Theory

Author: Steven J. Miller
Publisher: Princeton University Press
ISBN: 9780691120607
Format: PDF, Mobi
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In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.