Refined Large Deviation Limit Theorems

This monograph is mainly devoted to studying the asymptotic behavior of the probabilities of large deviations in the case when the famous Cramer's condition is not fulfilled. It provides the direct probabilistic method that enables one to construct expansions of increasing accuracy.

List of contents

Introduction 1. Asymptotic Expansions Taking into Account the Cases when the Number of Summands Comparable with the Sum is Less than or Equal to Two 2. Asymptotic Expansions of the Probabilities of Large Deviations and Non-Uniform Estimates of Remainders in CLT 3. Asymptotic Expansions Taking into Account the Cases when the Number of Summands Comparable with the Sum Does not Exceed a Fixed Integer 4. Limit Theorems on Large Deviations for Order Statistics 5. Large Deviations for I.I.D. Random Sums When Cramer's Condition is Fulfilled Only on a Finite Interval

About the author

Vinogradov\, Vladimir

Summary

This monograph is mainly devoted to studying the asymptotic behavior of the probabilities of large deviations in the case when the famous Cramer's condition is not fulfilled. It provides the direct probabilistic method that enables one to construct expansions of increasing accuracy.

Product details

• Authors: Vladimir Vinogradov, Vinogradov Vladimir
• Assisted by: Robert J. Elliott (Editor of the series)
• Publisher: Taylor and Francis
• Languages: English
• Product format: Hardback
• Released: 14.11.1994
• EAN: 9780582254992
• ISBN: 978-0-582-25499-2
• No. of pages: 224
• Weight: 385 g
• Series: Chapman & Hall/CRC Research Notes in Mathematics Series
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; MATHEMATICS / Probability & Statistics / General, Probability & statistics, Probability and statistics