Large Deviations for Discrete-Time Processes with Averaging / O. V. Gulinsky, A. Yu. Veretennikov.

Format:

Book

Author/Creator:

Gulinsky, O. V., author.

Veretennikov, A. Yu., author.

Language:

English

Subjects (All):

Large deviations.

Physical Description:

1 online resource (192 pages)

Edition:

Reprint 2018

Place of Publication:

Berlin ; Boston : De Gruyter, [2019]

Language Note:

In English.

Summary:

This book is mainly based on the Cramir--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.

Contents:

Frontmatter

Contents

Preface

Chapter 1. Introduction to large deviations

Chapter 2. Large deviations for the non-markovian recursive scheme with additive svhite noise'

Chapter 3. Large deviations for the recursive scheme with stationary disturbances

Chapter 4. Generalization of cramer's theorem

Chapter 5. Mixing for markov processes

Chapter 6. The averaging principle for some recursive stochastic schemes with state dependent noise

Chapter 7. Normal deviations

Chapter 8. Large deviations for markov processes

Chapter 9. Large deviations for stationary processes

Chapter 10. Large deviations for empirical measures

Chapter 11. Large deviations in averaging principle

Bibliography

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9783110917802

3110917807

OCLC:

1083621093