Modern Theory Of Summation Of Random Variables
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Modern Theory Of Summation Of Random Variables
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Author : Vladimir M. Zolotarev
language : en
Publisher: Walter de Gruyter
Release Date : 2011-09-06
Modern Theory Of Summation Of Random Variables written by Vladimir M. Zolotarev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-06 with Mathematics categories.
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Modern Theory Of Summation Of Random Variables
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Author : V. M. Zolotarev
language : en
Publisher:
Release Date :
Modern Theory Of Summation Of Random Variables written by V. M. Zolotarev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Modern Probability And Statistics
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Author : Vladimir M. Zolotarev
language : en
Publisher:
Release Date : 1997
Modern Probability And Statistics written by Vladimir M. Zolotarev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
A Modern Theory Of Random Variation
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Author : Patrick Muldowney
language : en
Publisher: John Wiley & Sons
Release Date : 2013-04-26
A Modern Theory Of Random Variation written by Patrick Muldowney and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-26 with Science categories.
A ground-breaking and practical treatment of probability and stochastic processes A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity. A Modern Theory of Random Variation is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation. Patrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.
Uniform Limit Theorems For Sums Of Independent Random Variables
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Author : Taĭvo Viktorovich Arak
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Uniform Limit Theorems For Sums Of Independent Random Variables written by Taĭvo Viktorovich Arak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Among the diverse constructions studied in modern probability theory, the scheme for summation of independent random variables occupies a special place. In the study of even this comparatively simple scheme it is possible to become familiar with the fundamental regularities characterizing the cumulative influence of a large number of random factors. Further, this abstract model is useful in many important practical situations. This book is devoted to the study of distributions of sums of independent random variables with minimal restrictions imposed on their distributions. The authors assume either that the distributions of the terms are concentrated on some finite interval to within a small mass, or that all the terms have the same, but arbitrary, distribution (or other conditions not connected with moment restrictions are introduced). Surprisingly, very substantive results are possible even under such a general statement of the problems.
Limit Theorems For Multi Indexed Sums Of Random Variables
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Author : Oleg Klesov
language : en
Publisher: Springer
Release Date : 2014-10-13
Limit Theorems For Multi Indexed Sums Of Random Variables written by Oleg Klesov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-13 with Mathematics categories.
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.
Probability And Statistics Volume I
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Author : Reinhard Viertl
language : en
Publisher: EOLSS Publications
Release Date : 2009-06-11
Probability And Statistics Volume I written by Reinhard Viertl and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-11 with categories.
Probability and Statistics theme is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme with contributions from distinguished experts in the field, discusses Probability and Statistics. Probability is a standard mathematical concept to describe stochastic uncertainty. Probability and Statistics can be considered as the two sides of a coin. They consist of methods for modeling uncertainty and measuring real phenomena. Today many important political, health, and economic decisions are based on statistics. This theme is structured in five main topics: Probability and Statistics; Probability Theory; Stochastic Processes and Random Fields; Probabilistic Models and Methods; Foundations of Statistics, which are then expanded into multiple subtopics, each as a chapter. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs
Reliability Is A New Science
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Author : Paolo Rocchi
language : en
Publisher: Springer
Release Date : 2017-07-13
Reliability Is A New Science written by Paolo Rocchi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-13 with Mathematics categories.
This work illustrates research conducted over a ten-year timespan and addresses a fundamental issue in reliability theory. This still appears to be an empirically disorganized field and the book suggests employing a deductive base in order to evolve reliability as a science. The study is in line with the fundamental work by Gnedenko. Boris Vladimirovich Gnedenko (1912 – 1995) was a Soviet mathematician who made significant contributions in various scientific areas. His name is especially associated with studies of dependability, for which he is often recognized as the 'father' of reliability theory. In the last few decades, this area has expanded in new directions such as safety, security, risk analysis and other fields, yet the book ‘Mathematical Methods in Reliability Theory’ written by Gnedenko with Alexander Soloviev and Yuri Bélyaev still towers as a pillar of the reliability sector’s configuration and identity. The present book proceeds in the direction opened by the cultural project of the Russian authors; in particular it identifies different trends in the hazard rate functions by means of deductive logic and demonstrations. Further, it arrives at multiple results by means of the entropy function, an original mathematical tool in the reliability domain. As such, it will greatly benefit all specialists in the field who are interested in unconventional solutions.
Limit Theorems For Associated Random Fields And Related Systems
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Author : Aleksandr Vadimovich Bulinskii
language : en
Publisher: World Scientific
Release Date : 2007
Limit Theorems For Associated Random Fields And Related Systems written by Aleksandr Vadimovich Bulinskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.). Contents: Random Systems with Covariance Inequalities; Moment and Maximal Inequalities; Central Limit Theorem; Almost Sure Convergence; Invariance Principles; Law of the Iterated Logarithm; Statistical Applications; Integral Functionals. Readership: Researchers in modern probability and statistics, graduate students and academic staff of the universities.
Mass Transportation Problems
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Author : Svetlozar T. Rachev
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-09
Mass Transportation Problems written by Svetlozar T. Rachev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-09 with Mathematics categories.
This is the first comprehensive account of the theory of mass transportation problems and its applications. In volume I, the authors systematically develop the theory of mass transportation with emphasis to the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems, and their various extensions. They discuss a variety of different approaches towards solutions of these problems and exploit the rich interrelations to several mathematical sciences--from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications to the mass transportation and mass transshipment problems to topics in applied probability, theory of moments and distributions with given marginals, queucing theory, risk theory of probability metrics and its applications to various fields, amoung them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations, stochastic algorithms and rounding problems. The book will be useful to graduate students and researchers in the fields of theoretical and applied probabilitry, operations research, computer science, and mathematical economics. The prerequisites for this book are graduate level probability theory and real and functional analysis.