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Limit Theorems for Large Deviations

Limit Theorems for Large Deviations
Author: L. Saulis
Publisher: Springer Science & Business Media
Total Pages: 241
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401135304

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"Et moi ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O.H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities 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 'e1:re of this series


Refined Large Deviation Limit Theorems

Refined Large Deviation Limit Theorems
Author: Vladimir Vinogradov
Publisher: CRC Press
Total Pages: 228
Release: 2023-06-14
Genre: Mathematics
ISBN: 100094834X

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This is a developing area of modern probability theory, which has applications in many areas. This volume is devoted to the systematic study of results on large deviations in situations where Cramér's condition on the finiteness of exponential moments may not be satisfied


Limit Theorems on Large Deviations for Markov Stochastic Processes

Limit Theorems on Large Deviations for Markov Stochastic Processes
Author: A.D. Wentzell
Publisher: Springer Science & Business Media
Total Pages: 192
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400918526

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In recent decades a new branch of probability theory has been developing intensively, namely, limit theorems for stochastic processes. As compared to classical limit theorems for sums of independent random variables, the generalizations are going here in two directions simultaneously. First, instead of sums of independent variables one considers stochastic processes belonging to certain broad classes. Secondly, instead of the distribution of a single sum - the distribution of the value of a stochastic process at one (time) point - or the joint distribution of the values of a process at a finite number of points, one considers distributions in an infinite-dimensional function space. For stochastic processes constructed, starting from sums of independent random variables, this is the same as considering the joint distribution of an unboundedly increasing number of sums.


Refined Large Deviation Limit Theorems

Refined Large Deviation Limit Theorems
Author: Vladimir Vinogradov
Publisher: CRC Press
Total Pages: 226
Release: 2023-06-14
Genre: Mathematics
ISBN: 1000941604

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This is a developing area of modern probability theory, which has applications in many areas. This volume is devoted to the systematic study of results on large deviations in situations where Cramér's condition on the finiteness of exponential moments may not be satisfied


Limit Theorems of Probability Theory

Limit Theorems of Probability Theory
Author: Yu.V. Prokhorov
Publisher: Springer Science & Business Media
Total Pages: 280
Release: 2013-03-14
Genre: Mathematics
ISBN: 3662041723

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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.


Universal Theory For Strong Limit Theorems Of Probability

Universal Theory For Strong Limit Theorems Of Probability
Author: Andrei N Frolov
Publisher: World Scientific
Total Pages: 204
Release: 2019-10-10
Genre: Mathematics
ISBN: 9811212848

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This is the first book which the universal approach to strong laws of probability is discussed in. The universal theories are described for three important objects of probability theory: sums of independent random variables, processes with independent increments and renewal processes. Further generalizations are mentioned. Besides strong laws, large deviations are of independent interest. The case of infinite variations is considered as well. Readers can examine appropriate techniques and methods. Optimality of conditions is discussed.


Large and Moderate Deviation Limit Theorems for Arbitrary Sequences of Random Variables with Applications

Large and Moderate Deviation Limit Theorems for Arbitrary Sequences of Random Variables with Applications
Author:
Publisher:
Total Pages: 11
Release: 1991
Genre:
ISBN:

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In this research project we have obtained several limit theorems for arbitrary and dependent sequences of random variables. The limit theorems considered in this project fall into three categories namely, Large deviation local limit theorems, Strong large deviation theorems and Strong moderate deviation theorems. These three categories are dependent in the sense they all are subcategories of large deviation theory. The theory of large deviations and its many users are well described in the book by Ellis (1985) and the monograph by Varadhan (1984). This work generalized several classical limit theorems that were obtained in the literature for independent and identically distributed random variables. In the next three sections we outline briefly the technical details of the work done under this contract.


Some Limit Theorems in Statistics

Some Limit Theorems in Statistics
Author: R. R. Bahadur
Publisher: SIAM
Total Pages: 48
Release: 1971-01-01
Genre: Mathematics
ISBN: 9781611970630

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A discussion of some topics in the theory of large deviations such as moment-generating functions and Chernoff's theorem, and of aspects of estimation and testing in large samples, such as exact slopes of test statistics.