Author : A. A. Borovkov
Publisher : Cambridge University Press
Page : 437 pages
File Size : 35,25 MB
Release : 2020-10-29
Category : Mathematics
ISBN : 1107074681
A systematic modern treatise on large deviation theory for random walks with light tails, from one of its key creators.
Author : A. A. Borovkov
Publisher : Cambridge University Press
Page : 437 pages
File Size : 25,40 MB
Release : 2020-10-29
Category : Mathematics
ISBN : 1108901204
This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.
Author : Aleksandr Alekseevich Borovkov
Publisher : Cambridge University Press
Page : 655 pages
File Size : 43,78 MB
Release : 2008
Category : Asymptotic expansions
ISBN :
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.
Author : A. A. Borovkov
Publisher : Cambridge University Press
Page : pages
File Size : 39,72 MB
Release : 2022-06-30
Category : Mathematics
ISBN : 100911560X
Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.
Author : Kevin Broughan
Publisher : Cambridge University Press
Page : 705 pages
File Size : 42,38 MB
Release : 2023-09-30
Category : Mathematics
ISBN : 1009384805
This third volume presents further equivalents to the Riemann hypothesis and explores its decidability.
Author : Kevin Broughan
Publisher : Cambridge University Press
Page : 706 pages
File Size : 13,19 MB
Release : 2023-09-30
Category : Mathematics
ISBN : 1009384775
This three-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 3 covers new arithmetic and analytic equivalences from numerous studies in the field, such as Rogers and Tao, and presents derivations which show whether the Riemann hypothesis is decidable.
Author : Hwa-Long Gau
Publisher : Cambridge University Press
Page : 556 pages
File Size : 38,44 MB
Release : 2021-08-05
Category : Mathematics
ISBN : 1108787606
Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.
Author : Lowell W. Beineke
Publisher : Cambridge University Press
Page : 400 pages
File Size : 18,1 MB
Release : 2021-06-03
Category : Mathematics
ISBN : 1108671071
Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book presents material on developments on graph algorithms and related concepts that will be of value to both mathematicians and computer scientists, at a level suitable for graduate students, researchers and instructors. The fifteen expository chapters, written by acknowledged international experts on their subjects, focus on the application of algorithms to solve particular problems. All chapters were carefully edited to enhance readability and standardize the chapter structure as well as the terminology and notation. The editors provide basic background material in graph theory, and a chapter written by the book's Academic Consultant, Martin Charles Golumbic (University of Haifa, Israel), provides background material on algorithms as connected with graph theory.
Author : Rabi Bhattacharya
Publisher : Springer Nature
Page : 396 pages
File Size : 44,33 MB
Release : 2021-09-20
Category : Mathematics
ISBN : 303078939X
This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov–Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.
Author : K A Borovkov
Publisher :
Page : 657 pages
File Size : 16,94 MB
Release : 2014-05-14
Category :
ISBN : 9781107398931
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.
