Stable Convergence And Stable Limit Theorems PDF Download
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Author | : Erich Häusler |
Publisher | : Springer |
Total Pages | : 231 |
Release | : 2015-06-09 |
Genre | : Mathematics |
ISBN | : 331918329X |
Download Stable Convergence and Stable Limit Theorems Book in PDF, ePub and Kindle
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
Author | : Ji Hyung Lee |
Publisher | : |
Total Pages | : 38 |
Release | : 2017 |
Genre | : |
ISBN | : |
Download Stable Limit Theorems for Empirical Processes Under Conditional Neighborhood Dependence Book in PDF, ePub and Kindle
This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets are indexed by the same set endowed with a neighborhood system. When the set of random variables satisfies CND, any two non-adjacent sets of random variables are conditionally independent given sigma algebras having indices in one of the two sets' neighborhood. Random variables with CND include those with conditional dependency graphs and a class of Markov random fields with a global Markov property. The CND property is useful for modeling cross-sectional dependence governed by a complex, large network. This paper provides two main results. The first result is a stable central limit theorem for a sum of random variables with CND. The second result is a Donsker-type result of stable convergence of empirical processes indexed by a class of functions satisfying a certain bracketing entropy condition when the random variables satisfy CND. When there are high-degree vertices, they potentially hamper normal approximation by causing widespread dependence among the random variables. Thus we generalize the results by approximating the sum of random variables by the sum conditioned on high-degree vertices so that stable limit results continue to hold even when the maximum degree of the neighborhood system diverges to infinity as the size of the system grows.
Author | : Alexander Bulinski |
Publisher | : World Scientific |
Total Pages | : 447 |
Release | : 2007-09-05 |
Genre | : Mathematics |
ISBN | : 9814474576 |
Download Limit Theorems For Associated Random Fields And Related Systems Book in PDF, ePub and Kindle
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 | : Gerd Christoph |
Publisher | : Wiley-VCH |
Total Pages | : 216 |
Release | : 1992-12-15 |
Genre | : Mathematics |
ISBN | : |
Download Covergence Theorems with a Stable Limit Law Book in PDF, ePub and Kindle
The book deals with Berry-Esseen-type inequalities, asymptotic expansions, non-uniform estimates, U-statistics, and the density problem.
Author | : Florin Avram |
Publisher | : |
Total Pages | : 302 |
Release | : 1986 |
Genre | : Central limit theorem |
ISBN | : |
Download Some Limit Theorems for Stationary Sequences with Infinite Or Finite Variance Book in PDF, ePub and Kindle
Author | : Oliver T Johnson |
Publisher | : World Scientific |
Total Pages | : 224 |
Release | : 2004-07-14 |
Genre | : Mathematics |
ISBN | : 1783260610 |
Download Information Theory And The Central Limit Theorem Book in PDF, ePub and Kindle
This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems.
Author | : David Ralph Beuerman |
Publisher | : |
Total Pages | : |
Release | : 1973 |
Genre | : |
ISBN | : |
Download Functional Stable Limit Theorems Book in PDF, ePub and Kindle
Author | : Ilya S. Molchanov |
Publisher | : Springer |
Total Pages | : 162 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540481117 |
Download Limit Theorems for Unions of Random Closed Sets Book in PDF, ePub and Kindle
The book concerns limit theorems and laws of large numbers for scaled unionsof independent identically distributed random sets. These results generalizewell-known facts from the theory of extreme values. Limiting distributions (called union-stable) are characterized and found explicitly for many examples of random closed sets. The speed of convergence in the limit theorems for unions is estimated by means of the probability metrics method.It includes the evaluation of distances between distributions of random sets constructed similarly to the well-known distances between distributions of random variables. The techniques include regularly varying functions, topological properties of the space of closed sets, Choquet capacities, convex analysis and multivalued functions. Moreover, the concept of regular variation is elaborated for multivalued (set-valued) functions. Applications of the limit theorems to simulation of random sets, statistical tests, polygonal approximations of compacts, limit theorems for pointwise maxima of random functions are considered. Several open problems are mentioned. Addressed primarily to researchers in the theory of random sets, stochastic geometry and extreme value theory, the book will also be of interest to applied mathematicians working on applications of extremal processes and their spatial counterparts. The book is self-contained, and no familiarity with the theory of random sets is assumed.
Author | : Rick Durrett |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2010-08-30 |
Genre | : Mathematics |
ISBN | : 113949113X |
Download Probability Book in PDF, ePub and Kindle
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 | : P. Jeganathan |
Publisher | : |
Total Pages | : 0 |
Release | : 2006 |
Genre | : |
ISBN | : |
Download Limit Theorems for Functionals of Sums that Converge to Fractional Stable Motions Book in PDF, ePub and Kindle