A Large Deviation Principle for U-statistics in Banach Spaces PDF Download
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Author: Yuri V. Borovskikh
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Author: Yuri V. Borovskikh
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
Author: D.W. Stroock
Publisher: Springer Science & Business Media
ISBN: 1461385148
Category : Mathematics
Languages : en
Pages : 204
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Book Description
These notes are based on a course which I gave during the academic year 1983-84 at the University of Colorado. My intention was to provide both my audience as well as myself with an introduction to the theory of 1arie deviations • The organization of sections 1) through 3) owes something to chance and a great deal to the excellent set of notes written by R. Azencott for the course which he gave in 1978 at Saint-Flour (cf. Springer Lecture Notes in Mathematics 774). To be more precise: it is chance that I was around N. Y. U. at the time'when M. Schilder wrote his thesis. and so it may be considered chance that I chose to use his result as a jumping off point; with only minor variations. everything else in these sections is taken from Azencott. In particular. section 3) is little more than a rewrite of his exoposition of the Cramer theory via the ideas of Bahadur and Zabel. Furthermore. the brief treatment which I have given to the Ventsel-Freidlin theory in section 4) is again based on Azencott's ideas. All in all. the biggest difference between his and my exposition of these topics is the language in which we have written. However. another major difference must be mentioned: his bibliography is extensive and constitutes a fine introduction to the available literature. mine shares neither of these attributes. Starting with section 5).
Author: Yu. V. Borovskikh
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112318897
Category : Mathematics
Languages : en
Pages : 436
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Book Description
No detailed description available for "U-Statistics in Banach Spaces".
Author: Vladimir S. Korolyuk
Publisher: Springer Science & Business Media
ISBN: 9401735158
Category : Mathematics
Languages : en
Pages : 558
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Book Description
The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.
Author: Alejandro D. de Acosta
Publisher:
ISBN: 1009063359
Category : Mathematics
Languages : en
Pages : 264
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Book Description
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
Author: B. Grigelionis
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112319028
Category : Mathematics
Languages : en
Pages : 624
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Book Description
No detailed description available for "PROB. TH. MATH. ST. ( GRIGELIONIS) VOL. 2 PROC.5/1989 E-BOOK".
Author: Joergen Hoffmann-Joergensen
Publisher: Birkhäuser
ISBN: 3034880596
Category : Mathematics
Languages : en
Pages : 343
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Book Description
The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970s. Many of the problems that motivated researchers at that time were solved. But the powerful new tools created for their solution turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new approach to the study of aspects of Lévy processes and Markov processes in general. The papers in this book reflect these broad categories. The volume thus will be a valuable resource for postgraduates and reseachers in probability theory and mathematical statistics.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Frank Hollander
Publisher: American Mathematical Soc.
ISBN: 9780821844359
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
Author:
Publisher:
ISBN:
Category : Statistics
Languages : en
Pages : 722
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Book Description
