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| Author | : Aleksandr Alekseevich Borovkov |
| Publisher | : Cambridge University Press |
| Total Pages | : 655 |
| Release | : 2008 |
| Genre | : 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 |
| Total Pages | : 437 |
| Release | : 2020-10-29 |
| Genre | : 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 | : K A Borovkov |
| Publisher | : |
| Total Pages | : 657 |
| Release | : 2014-05-14 |
| Genre | : |
| ISBN | : 9781107398931 |
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.
| Author | : Aleksandr Alekseevich Borovkov |
| Publisher | : |
| Total Pages | : 625 |
| Release | : 2008 |
| Genre | : Asymptotic expansions |
| ISBN | : 9781461941576 |
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 |
| Total Pages | : 437 |
| Release | : 2020-10-29 |
| Genre | : Mathematics |
| ISBN | : 1107074681 |
A systematic modern treatise on large deviation theory for random walks with light tails, from one of its key creators.
| Author | : Stanford University. Department of Statistics |
| Publisher | : |
| Total Pages | : 38 |
| Release | : 1988 |
| Genre | : |
| ISBN | : |
| Author | : Yves Benoist |
| Publisher | : Springer |
| Total Pages | : 319 |
| Release | : 2016-10-20 |
| Genre | : Mathematics |
| ISBN | : 3319477218 |
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 | : Serguei Popov |
| Publisher | : Cambridge University Press |
| Total Pages | : 224 |
| Release | : 2021-03-18 |
| Genre | : Mathematics |
| ISBN | : 1108472451 |
A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
| Author | : Sidney Redner |
| Publisher | : Cambridge University Press |
| Total Pages | : 332 |
| Release | : 2001-08-06 |
| Genre | : Business & Economics |
| ISBN | : 0521652480 |
The basic theory presented in a way which emphasizes intuition, problem-solving and the connections with other fields.
| Author | : Wolfgang Woess |
| Publisher | : Cambridge University Press |
| Total Pages | : 350 |
| Release | : 2000-02-13 |
| Genre | : Mathematics |
| ISBN | : 0521552923 |
The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
