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Author : A.A. Borovkov
Publisher : Cambridge University Press
Page : 437 pages
File Size : 44,7 Mb
Release : 2020-10-29
Category : Mathematics
ISBN : 9781107074682
A systematic modern treatise on large deviation theory for random walks with light tails, from one of its key creators.
Author : K A Borovkov,Aleksandr Alekseevich Borovkov
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2013-09-30
Category : Electronic
ISBN : 1299909280
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.
Author : Aleksandr Alekseevich Borovkov
Publisher : Unknown
Page : 625 pages
File Size : 49,6 Mb
Release : 2008
Category : Asymptotic expansions
ISBN : 1461941571
This monograph is devoted to studying the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks, with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. It presents a unified and systematic exposition.
Author : Aleksandr Alekseevich Borovkov
Publisher : Cambridge University Press
Page : 655 pages
File Size : 49,8 Mb
Release : 2008
Category : Asymptotic expansions
ISBN : 8210379456XXX
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 : 128 pages
File Size : 43,9 Mb
Release : 2022-06-30
Category : Mathematics
ISBN : 9781009115605
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 : 50,5 Mb
Release : 2023-09-30
Category : Mathematics
ISBN : 9781009384803
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 : 47,9 Mb
Release : 2023-09-30
Category : Mathematics
ISBN : 9781009384773
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 : Rabi Bhattacharya,Edward C. Waymire
Publisher : Springer Nature
Page : 396 pages
File Size : 47,7 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9783030789398
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 : Allan Gut
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 42,5 Mb
Release : 2009-04-03
Category : Mathematics
ISBN : 9780387878355
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."
Author : Marcelo Aguiar,Swapneel Mahajan
Publisher : Cambridge University Press
Page : 897 pages
File Size : 44,8 Mb
Release : 2022-10-31
Category : Mathematics
ISBN : 9781009243735
The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.
Author : Wolfgang Lay
Publisher : Cambridge University Press
Page : 316 pages
File Size : 55,7 Mb
Release : 2024-05-23
Category : Mathematics
ISBN : 9781009546584
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaffé, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Author : Yuen-Kwok Chan
Publisher : Cambridge University Press
Page : 627 pages
File Size : 49,9 Mb
Release : 2021-05-27
Category : Mathematics
ISBN : 9781108835435
This book provides a systematic and general theory of probability within the framework of constructive mathematics.
Author : Jayakrishnan Nair,Adam Wierman,Bert Zwart
Publisher : Cambridge University Press
Page : 265 pages
File Size : 48,8 Mb
Release : 2022-06-09
Category : Business & Economics
ISBN : 9781316511732
An accessible yet rigorous package of probabilistic and statistical tools for anyone who must understand or model extreme events.
Author : George Herbert Weiss
Publisher : Elsevier Science & Technology
Page : 388 pages
File Size : 52,9 Mb
Release : 1994
Category : Computers
ISBN : UOM:39015032947924
Paperback. Both the formalism and many of the attendant ideas related to the random walk lie at the core of a significant fraction of contemporary research in statistical physics. In the language of physics the random walk can be described as a microscopic model for transport processes which have some element of randomness. The starting point of nearly all analyses of transport in disordered media is to be found in one or another type of random walk model. Mathematical formalism based on the theory of random walks is not only pervasive in a number of areas of physics, but also finds application in many areas of chemistry. The random walk has also been applied to the study of a number of biological phenomena.Despite the obvious importance of random walks in these and other applications there are few books devoted to the subject. This is therefore a timely introduction to the subject which will be welcomed by students and more senior researchers who have
Author : Thomas Michelitsch,Alejandro Perez Riascos,Bernard Collet,Andrzej Nowakowski,Franck Nicolleau
Publisher : John Wiley & Sons
Page : 294 pages
File Size : 54,5 Mb
Release : 2019-04-10
Category : Technology & Engineering
ISBN : 9781119608219
This book analyzes stochastic processes on networks and regular structures such as lattices by employing the Markovian random walk approach. Part 1 is devoted to the study of local and non-local random walks. It shows how non-local random walk strategies can be defined by functions of the Laplacian matrix that maintain the stochasticity of the transition probabilities. A major result is that only two types of functions are admissible: type (i) functions generate asymptotically local walks with the emergence of Brownian motion, whereas type (ii) functions generate asymptotically scale-free non-local “fractional” walks with the emergence of Lévy flights. In Part 2, fractional dynamics and Lévy flight behavior are analyzed thoroughly, and a generalization of Pólya's classical recurrence theorem is developed for fractional walks. The authors analyze primary fractional walk characteristics such as the mean occupation time, the mean first passage time, the fractal scaling of the set of distinct nodes visited, etc. The results show the improved search capacities of fractional dynamics on networks.
