Large Deviations for Discrete-Time Processes with Averaging
VSP International Science Publishers (Verlag)
978-90-6764-148-7 (ISBN)
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01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.
This book is mainly based on the Cramér--Chernoff renowned theorem, which deals with the 'rough' logarithmic asymptotics of the distribution of sums of independent, identically distributed random variables. The authors approach primarily the extensions of this theory to dependent, and in particular, nonmarkovian cases on function spaces. Recurrent algorithms of identification and adaptive control form the main examples behind the large deviation problems in this volume.
The first part of the book exploits some ideas and concepts of the martingale approach, especially the concept of the stochastic exponential. The second part of the book covers Freindlin's approach, based on the Frobenius-type theorems for positive operators, which prove to be effective for the cases in consideration.
INTRODUCTION TO LARGE DEVIATIONS
Cramér-type results (the classical Cramér theorem; the extensions of Cramér's theorem)
Large deviations on the space of probability measures
Application to statistical mechanics
Basic large deviations concepts
Large deviations for sums of independent and identically distributed variables in function space
Applications to recursive estimation and control theory
LARGE DEVIATIONS FOR NON-MARKOVIAN RECURSIVE SCHEME WITH ADDITITIVE 'WHITE NOISE'
LARGE DEVIATION FOR THE RECURSIVE SCHEME WITH STATIONARY DISTURBANCES
Large deviations for the sums of stationary
Large deviations for recursive scheme with the Wold-type disturbances
GENERALIZATION OF CRAMÉR'S THEOREM
Large deviations for sums of stationary sequence
Large deviations for sums of semimartingales
MIXING FOR MARKOV PROCESSES
Definitions
Main results
Preliminary results
Proofs of theorems 5.1--5.6
Mixing coefficients for recursive procedure
THE AVERAGING PRINCIPLE FOR SOME RECURSIVE SCHEMES
NORMAL DEVIATIONS
LARGE DEVIATIONS FOR MARKOV PROCESSES
Introduction
Examples
Markovian noncompact case
Auxiliary results
Proofs of theorems 8.6--8.8
Proof of theorem 8.9
LARGE DEVIATIONS FOR STATIONARY PROCESSES
Compact nonsingular case
Noncompact nonsingular case
LARGE DEVIATIONS FOR EMPIRICAL MEASURES
Introduction
Markov chain with Doeblin-type condition
Noncompact Markov case
Stationary compact case
Stationary noncompact case
LARGE DEVIATIONS FOR EMPIRICAL MEASURES
Compact case
Noncompact case
| Erscheint lt. Verlag | 1.8.1993 |
|---|---|
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 480 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Medizin / Pharmazie ► Medizinische Fachgebiete ► Schmerztherapie | |
| ISBN-10 | 90-6764-148-0 / 9067641480 |
| ISBN-13 | 978-90-6764-148-7 / 9789067641487 |
| Zustand | Neuware |
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