Stopped Random Walks
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Stopped Random Walks
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Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Stopped Random Walks written by Allan Gut 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 2009-04-03 with Mathematics categories.
Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Examples are sequential analysis, queueing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of counters. Stopped Random Walks: Limit Theorems and Applications shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimensional random walks, and to how these results are useful in various applications. This second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter examines nonlinear renewal processes in order to present the analagous theory for perturbed random walks, modeled as a random walk plus “noise”.
Stopped Random Walks
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Author : Allan Gut
language : en
Publisher: Springer
Release Date : 2014-01-15
Stopped Random Walks written by Allan Gut and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Probability A Graduate Course
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Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-16
Probability A Graduate Course written by Allan Gut 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 2006-03-16 with Mathematics categories.
"I know it's trivial, but I have forgotten why". This is a slightly exaggerated characterization of the unfortunate attitude of many mathematicians toward the surrounding world. The point of departure of this book is the opposite. This textbook on the theory of probability is aimed at graduate students, with the ideology that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to chapters on inequalities, characteristic functions, convergence, followed by the three main subjects, the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The main feature of this book is the combination of rigor and detail. Instead of being sketchy and leaving lots of technicalities to be filled in by the reader or as easy exercises, a more solid foundation is obtained by providing more of those not so trivial matters and by integrating some of those not so simple exercises and problems into the body of text. Some results have been given more than one proof in order to illustrate the pros and cons of different approaches. On occasion we invite the reader to minor extensions, for which the proofs reduce to minor modifications of existing ones, with the aim of creating an atmosphere of a dialogue with the reader (instead of the more typical monologue), in order to put the reader in the position to approach any other text for which a solid probabilistic foundation is necessary. Allan Gut is a professor of Mathematical Statistics at Uppsala University, Uppsala, Sweden. He is the author of the Springer monograph "Stopped Random Walks" (1988), the Springer textbook "An Intermediate Course in Probability" (1995), and has published around 60 articles in probability theory. His interest in attracting amore general audience to the beautiful world of probability has been manifested in his Swedish popular science book Sant eller Sannolikt ("True or Probable"), Norstedts förlag (2002). From the reviews: "This is more substantial than the usual graduate course in probability; it contains many useful and interesting details that previously were scattered around the literature and gives clear evidence that the writer has a great deal of experience in the area." Short Book Reviews of the International Statistical Institute, December 2005 "...This book is a readable, comprehensive, and up-to-date introductory textbook to probability theory with emphasis on limit theorems for sums and extremes of random variables. The purchase is worth its price." Journal of the American Statistical Association, June 2006
The Queue As A Stopped Random Walk
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Author : Elena Marie Caruso
language : en
Publisher:
Release Date : 1968
The Queue As A Stopped Random Walk written by Elena Marie Caruso and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Queuing theory categories.
Very First Steps In Random Walks
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Author : Norbert Henze
language : en
Publisher: Springer Nature
Release Date : 2025-02-11
Very First Steps In Random Walks written by Norbert Henze and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-11 with Mathematics categories.
With this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter. Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Locally Perturbed Random Walks
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Author : Alexander Iksanov
language : en
Publisher: Springer Nature
Release Date : 2025-05-23
Locally Perturbed Random Walks written by Alexander Iksanov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-23 with Mathematics categories.
This monograph provides a comprehensive overview of locally perturbed random walks, tools used for their analysis, and current research on their applications. The authors present the material in a self-contained manner, providing strong motivation in Chapter One with illustrative examples of locally perturbed random walks and an introduction of the mathematical tools that are used throughout the book. Chapter Two shows the construction of various stochastic processes that serve as scaling limits for locally perturbed random walks, particularly focusing on reflected and skewed processes. In Chapter Three, the authors prove various limit theorems for these perturbed random walks. The final chapter serves as an appendix that collects essential background material for readers who wish to understand the arguments more deeply. Locally Perturbed Random Walks will appeal to researchers interested in this area within modern probability theory. It is also accessible to students who have taken a second course in probability.
Asymptotic Analysis Of Random Walks Light Tailed Distributions
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Author : A. A. Borovkov
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-29
Asymptotic Analysis Of Random Walks Light Tailed Distributions written by A. A. 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 2020-10-29 with Mathematics categories.
A systematic modern treatise on large deviation theory for random walks with light tails, from one of its key creators.
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].
Renewal Theory For Perturbed Random Walks And Similar Processes
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Author : Alexander Iksanov
language : en
Publisher: Birkhäuser
Release Date : 2016-12-09
Renewal Theory For Perturbed Random Walks And Similar Processes written by Alexander Iksanov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-09 with Mathematics categories.
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters four and five address branching random walks and the Bernoulli sieve, respectively, and their connection to the results of the previous chapters. With many motivating examples, this book appeals to both theoretical and applied probabilists.
Probability
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Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2013
Probability written by Allan Gut 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 with Mathematics categories.
Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.