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| Author | : Yu.V. Prokhorov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662041723 |
A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.
| Author | : Hans Fischer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 415 |
| Release | : 2010-10-08 |
| Genre | : Mathematics |
| ISBN | : 0387878572 |
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
| Author | : Emmanuel Lesigne |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821837141 |
Everyone knows some of the basics of probability, perhaps enough to play cards. Beyond the introductory ideas, there are many wonderful results that are unfamiliar to the layman, but which are well within our grasp to understand and appreciate. Some of the most remarkable results in probability are those that are related to limit theorems--statements about what happens when the trial is repeated many times. The most famous of these is the Law of Large Numbers, which mathematicians,engineers, economists, and many others use every day. In this book, Lesigne has made these limit theorems accessible by stating everything in terms of a game of tossing of a coin: heads or tails. In this way, the analysis becomes much clearer, helping establish the reader's intuition aboutprobability. Moreover, very little generality is lost, as many situations can be modelled from combinations of coin tosses. This book is suitable for anyone who would like to learn more about mathematical probability and has had a one-year undergraduate course in analysis.
| Author | : Henry McKean |
| Publisher | : Cambridge University Press |
| Total Pages | : 487 |
| Release | : 2014-11-27 |
| Genre | : Computers |
| ISBN | : 1107053218 |
A leading authority sheds light on a variety of interesting topics in which probability theory plays a key role.
| Author | : Rick Durrett |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2010-08-30 |
| Genre | : Mathematics |
| ISBN | : 113949113X |
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
| Author | : Peter Eichelsbacher |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 317 |
| Release | : 2013-04-23 |
| Genre | : Mathematics |
| ISBN | : 3642360688 |
Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.
| Author | : Marc Hallin |
| Publisher | : Springer |
| Total Pages | : 326 |
| Release | : 2015-04-07 |
| Genre | : Mathematics |
| ISBN | : 3319124420 |
This Festschrift in honour of Paul Deheuvels’ 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems. The book brings together contributions from invited international experts to provide an up-to-date survey of the field. Written in textbook style, this collection of original material addresses researchers, PhD and advanced Master students with a solid grasp of mathematical statistics and probability theory.
| Author | : Shoumei Li |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 414 |
| Release | : 2002-10-31 |
| Genre | : Mathematics |
| ISBN | : 9781402009181 |
This book presents a clear, systematic treatment of convergence theorems of set-valued random variables (random sets) and fuzzy set-valued random variables (random fuzzy sets). Topics such as strong laws of large numbers and central limit theorems, including new results in connection with the theory of empirical processes are covered. The author's own recent developments on martingale convergence theorems and their applications to data processing are also included. The mathematical foundations along with a clear explanation such as Hölmander's embedding theorem, notions of various convergence of sets and fuzzy sets, Aumann integrals, conditional expectations, selection theorems, measurability and integrability arguments for both set-valued and fuzzy set-valued random variables and newly obtained optimizations techniques based on invariant properties are also given.
| Author | : Alexander Bulinski |
| Publisher | : World Scientific |
| Total Pages | : 447 |
| Release | : 2007-09-05 |
| Genre | : Mathematics |
| ISBN | : 9814474576 |
This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).
| Author | : Dmitriĭ Sergeevich Silʹvestrov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 426 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9781852337773 |
Limit theorems for stochastic processes are an important part of probability theory and mathematical statistics and one model that has attracted the attention of many researchers working in the area is that of limit theorems for randomly stopped stochastic processes.This volume is the first to present a state-of-the-art overview of this field, with many of the 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. A survey of the literature and an extended bibliography of works in the area are also provided.The coverage is thorough, streamlined and arranged according to difficulty for use as an upper-level text if required. It is an essential reference for theoretical and applied researchers in the fields of probability and statistics that will contribute to the continuing extensive studies in the area and remain relevant for years to come.
