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| Author | : Vladimir M. Zolotarev |
| Publisher | : Walter de Gruyter |
| Total Pages | : 429 |
| Release | : 2011-09-06 |
| Genre | : Mathematics |
| ISBN | : 3110936534 |
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.
| Author | : V. M. Zolotarev |
| Publisher | : |
| Total Pages | : |
| Release | : |
| Genre | : |
| ISBN | : 9783110631241 |
| Author | : Vladimir M. Zolotarev |
| Publisher | : |
| Total Pages | : 412 |
| Release | : 1997 |
| Genre | : |
| ISBN | : |
| Author | : V.V. Petrov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642658091 |
The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari ables" by B.V. Gnedenko and A.N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I.A. Ibragi mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity
| Author | : Taĭvo Viktorovich Arak |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 236 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : 9780821831182 |
Among the diverse constructions studied in modern probability theory, the scheme for summation of independent random variables occupies a special place. This book presents a study of distributions of sums of independent random variables with minimal restrictions imposed on their distributions.
| Author | : Boris V. Gnedenko |
| Publisher | : CRC Press |
| Total Pages | : 282 |
| Release | : 2020-07-24 |
| Genre | : Mathematics |
| ISBN | : 1000141179 |
This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.
| Author | : Reinhard Viertl |
| Publisher | : EOLSS Publications |
| Total Pages | : 410 |
| Release | : 2009-06-11 |
| Genre | : |
| ISBN | : 1848260520 |
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
| Author | : Bert E. Fristedt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 780 |
| Release | : 1996-12-23 |
| Genre | : Mathematics |
| ISBN | : 9780817638078 |
Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
| Author | : Emanuel Parzen |
| Publisher | : |
| Total Pages | : 666 |
| Release | : 1960 |
| Genre | : Probabilities |
| ISBN | : |
| Author | : Bert E. Fristedt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 775 |
| Release | : 2013-11-21 |
| Genre | : Mathematics |
| ISBN | : 1489928375 |
Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
