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Author : Aleksandr Alekseevich Borovkov
Publisher : Cambridge University Press
Page : 655 pages
File Size : 43,5 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 : K A Borovkov,Aleksandr Alekseevich Borovkov
Publisher : Unknown
Page : 657 pages
File Size : 54,5 Mb
Release : 2014-05-14
Category : Electronic
ISBN : 1107398932
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 : 53,6 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 : A.A. Borovkov
Publisher : Cambridge University Press
Page : 437 pages
File Size : 49,7 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 : George Herbert Weiss
Publisher : Elsevier Science & Technology
Page : 388 pages
File Size : 49,6 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 : Sidney Redner
Publisher : Cambridge University Press
Page : 332 pages
File Size : 46,8 Mb
Release : 2001-08-06
Category : Business & Economics
ISBN : 9780521652483
The basic theory presented in a way which emphasizes intuition, problem-solving and the connections with other fields.
Author : Frank Spitzer
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 41,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475742299
This book is devoted exclusively to a very special class of random processes, namely, to random walk on the lattice points of ordinary Euclidian space. The author considers this high degree of specialization worthwhile because the theory of such random walks is far more complete than that of any larger class of Markov chains. Almost 100 pages of examples and problems are included.
Author : Loïc Chaumont,Andreas E. Kyprianou
Publisher : Springer Nature
Page : 354 pages
File Size : 43,8 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030833091
This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.
Author : Allan Gut
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 54,9 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 : A. A. Borovkov
Publisher : Cambridge University Press
Page : 128 pages
File Size : 42,5 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 : Yves Benoist,Jean-François Quint
Publisher : Springer
Page : 323 pages
File Size : 52,7 Mb
Release : 2016-10-20
Category : Mathematics
ISBN : 9783319477213
The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Author : Michael N. Barber,B. W. Ninham
Publisher : CRC Press
Page : 190 pages
File Size : 50,9 Mb
Release : 1970
Category : Mathematics
ISBN : 067702620X
Author : Donald Dawson,Rafal Kulik,Mohamedou Ould Haye,Barbara Szyszkowicz,Yiqiang Zhao
Publisher : Springer
Page : 406 pages
File Size : 45,9 Mb
Release : 2015-11-12
Category : Mathematics
ISBN : 9781493930760
This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.
Author : Gregory F. Lawler
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 41,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475721379
A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.
Author : Jacob Willem Cohen
Publisher : John Wiley & Sons
Page : 410 pages
File Size : 55,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9051990863
In 1983 O.J. Boxma and the author have published a research monograph on Boundary Value Problems in Queueing System Analysis. The continuation of that research is described in the present monograph. The technique developed in the 1983-monograph has appeared to be quite powerful in the construction of explicit expressions for the generating functions and/or Laplace-Stieltjes transforms of characteristic distributions needed in the performance evaluation of stoachistic models stemming from computer system and telecommunication engineering. The book covers the following topics: One- Dimensional Random Walks; Two-Dimensional Random Walks; the Two-Dimensional Workload Process; and the N-Dimensional Random Walk.
