Download or read book Stopped Random Walks written by Allan Gut and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, queuing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of contours. 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-dimenstional 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."
Download or read book Stopped Random Walks written by Allan Gut and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: My first encounter with renewal theory and its extensions was in 1967/68 when I took a course in probability theory and stochastic processes, where the then recent book Stochastic Processes by Professor N.D. Prabhu was one of the requirements. Later, my teacher, Professor Carl-Gustav Esseen, gave me some problems in this area for a possible thesis, the result of which was Gut (1974a). Over the years I have, on and off, continued research in this field. During this time it has become clear that many limit theorems can be obtained with the aid of limit theorems for random walks indexed by families of positive, integer valued random variables, typically by families of stopping times. During the spring semester of 1984 Professor Prabhu visited Uppsala and very soon got me started on a book focusing on this aspect. I wish to thank him for getting me into this project, for his advice and suggestions, as well as his kindness and hospitality during my stay at Cornell in the spring of 1985. Throughout the writing of this book I have had immense help and support from Svante Janson. He has not only read, but scrutinized, every word and every formula of this and earlier versions of the manuscript. My gratitude to him for all the errors he found, for his perspicacious suggestions and remarks and, above all, for what his unusual personal as well as scientific generosity has meant to me cannot be expressed in words.
Download or read book Renewal Theory for Perturbed Random Walks and Similar Processes written by Alexander Iksanov and published by Birkhäuser. This book was released on 2016-12-09 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 2001 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Applied Probability written by and published by . This book was released on 2003 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limit Theorems for Randomly Stopped Stochastic Processes written by Dmitrii S. Silvestrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail. Its coverage is thorough, streamlined and arranged according to difficulty.
Download or read book Sojourns in Probability Theory and Statistical Physics III written by Vladas Sidoravicius and published by Springer Nature. This book was released on 2019-10-17 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.
Download or read book Journal of Statistical Planning and Inference written by North-Holland Publishing Company and published by . This book was released on 1999 with total page 1214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Walks Critical Phenomena and Triviality in Quantum Field Theory written by Roberto Fernandez and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.
Download or read book From Random Walks to Random Matrices written by Jean Zinn-Justin and published by Oxford University Press, USA. This book was released on 2019-06-27 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models, and in consequence develops our understanding of the fundamental nature of the universe. This books offers an overview of major areas covering the recent developments in modern theoretical physics. Each chapter introduces a new key topic and develops the discussion in a self-contained manner. At the same time the selected topics have common themes running throughout the book, which connect the independent discussions. The main themes are renormalization group, fixed points, universality, and continuum limit, which open and conclude the work. The development of modern theoretical physics has required important concepts and novel mathematical tools, examples discussed in the book include path and field integrals, the notion of effective quantum or statistical field theories, gauge theories, and the mathematical structure at the basis of the interactions in fundamental particle physics, including quantization problems and anomalies, stochastic dynamical equations, and summation of perturbative series.
Download or read book Stochastic Processes in Physics Chemistry and Biology written by Jan A. Freund and published by Springer Science & Business Media. This book was released on 2000-10-04 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until - cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences - especially chemistry and biology - based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise-- hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.
Download or read book Journal of Research of the National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1956 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Symposium on the Astronomy and Physics of Meteors Held at Smithsonian Astrophysical Observatory Cambridge Massachusetts 28 August 1 September 1961 written by and published by . This book was released on 1962 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non homogeneous Random Walks written by Mikhail Menshikov and published by Cambridge University Press. This book was released on 2016-12-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.
Download or read book Quantum Physics written by J. Glimm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to one problem and to three audiences. The problem is the mathematical structure of modem physics: statistical physics, quantum mechanics, and quantum fields. The unity of mathemati cal structure for problems of diverse origin in physics should be no surprise. For classical physics it is provided, for example, by a common mathematical formalism based on the wave equation and Laplace's equation. The unity transcends mathematical structure and encompasses basic phenomena as well. Thus particle physicists, nuclear physicists, and con densed matter physicists have considered similar scientific problems from complementary points of view. The mathematical structure presented here can be described in various terms: partial differential equations in an infinite number of independent variables, linear operators on infinite dimensional spaces, or probability theory and analysis over function spaces. This mathematical structure of quantization is a generalization of the theory of partial differential equa tions, very much as the latter generalizes the theory of ordinary differential equations. Our central theme is the quantization of a nonlinear partial differential equation and the physics of systems with an infinite number of degrees of freedom. Mathematicians, theoretical physicists, and specialists in mathematical physics are the three audiences to which the book is addressed. Each of the three parts is written with a different scientific perspective.
