Refined Large Deviation Limit Theorems

Vinogradov\, Vladimir

• 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