A wide-ranging, extensive overview of modern mathematical statistics, this work reflects the current state of the field while being succinct and easy to grasp. The mathematical presentation is coherent and rigorous throughout. The author presents classical results and methods that form the basis of modern statistics, and examines the foundations o
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.
Probability theory forms the basis of mathematical statistics, and has applications in many related areas. This comprehensive book tackles the principal problems and advanced questions of probability theory in 21 self-contained chapters, which are presented in logical order, but are also easy to deal with individually. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results. Probability theory is currently an extremely active area of research internationally, and the importance of the Russian school in the development of the subject has long been recognized. The frequent references to Russian literature throughout this work lend a fresh dimension to the book, and make it an invaluable source of reference for Western researchers and advanced students in probability related subjects.
First published in 1939, this resource sets forth cornerstone concepts of recovery from alcoholism and tells the stories of men and women who have overcome the disease.
A wide-ranging, extensive overview of modern mathematical statistics, this work reflects the current state of the field while being succinct and easy to grasp. The mathematical presentation is coherent and rigorous throughout. The author presents classical results and methods that form the basis of modern statistics, and examines the foundations o
The EZ Big Book of Alcoholics Anonymous is a page-by-page translation of the original Alcoholics Anonymous published by AA founder Bill Wilson in the 1930s. It is intended to carry the AA message to modern readers who find the original Big Book hard to digest for any reason. The language is gender-neutral, and references to spirituality are more inclusive. The book shows you how to: Quit drinking Find a personal Higher Power Livei n the now Face problems fearlessly Discover the real you Make great friends in AA Advance Reviews The anonymous author of this work has taken a bold step by updating the language of the original Big Book, which has barely changed since its introduction in 1939. John Elm, PhD, AA member Finally, a version of the Big Book has arrived that's as inclusive as the program itself. The language does not assume the reader is male or Christian. Jules Cardello, LMSW, Social Worker The simple, direct writing makes the message of the Big Book much easier to understand without any loss of meaning. Anonymous AA Member
Probability theory forms the basis of mathematical statistics, and has applications in many related areas. This comprehensive book tackles the principal problems and advanced questions of probability theory in 21 self-contained chapters, which are presented in logical order, but are also easy to deal with individually. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results. Probability theory is currently an extremely active area of research internationally, and the importance of the Russian school in the development of the subject has long been recognized. The frequent references to Russian literature throughout this work lend a fresh dimension to the book, and make it an invaluable source of reference for Western researchers and advanced students in probability related subjects.
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.
This book covers the history of lasers with nuclear pumping (Nuclear Pumped Lasers, NPLs). This book showcases the most important results and stages of NPL development in The Russian Federal Nuclear Center (VNIIEF) as well as other Russian and international laboratories, including laboratories in the United States. The basic science and technology behind NPLs along with potential applications are covered throughout the book. As the first comprehensive discussion of NPLs, students, researchers, and application engineers interested in high energy lasers will find this book to be an extremely valuable source of information about these unique lasers.
Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().
Et moi, ...* si j'avait su comment en revcnir. One service mathematics has rendered the je n'y scrais point aile.' human race. It has put common sense back where it belongs, on the topmost shclf next Jules Verne to the dusty canister labdlcd 'discarded non· The series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
This book is dedicated to the fundamental physical aspects of stability, the influence of structural defects on the properties and structural phase transformations of BCC alloys. The authors present patterns that occur in the structural-phase states of functional alloys with low stability or instability under thermal cycling effects. Structural-phase transformations and the physical laws governing the influence of the thermomechanical effect on the properties of alloys are examined to advance development of technological processes for processing functional materials. Features: Studies the correlation between structural phase states and changes in the physico-mechanical properties of intermetallic compounds Explores the influence of thermomechanical cycling on the properties of functional alloys Details low-stability pretransition states in alloys
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