Refined Large Deviation Limit Theorems

Dr. Vladimir Vinogradov is a Professor of Mathematics at Ohio University in Athens, Ohio. He earned his M.Sc. in Mathematics and Ph.D. in Probability and Statistics from Moscow State University with his dissertation published in his monograph "Refined Large Deviation Limit Theorems". Professor Vinogradov has taught in various post-secondary institutions of Canada, Japan, Russia and U.S.A., and held an NSERC Canada postdoctoral fellowship at Carleton University. His research focuses on various topics of Probability Theory, Stochastic Processes, Mathematical Statistics, Analysis and Financial Mathematics. Professor Vinogradov has published articles in many professional journals and presents frequently at national and international conferences. He has been recipient of a British Columbia – Asia Pacific Scholars' Award, and served on the Ontario Graduate Scholarships Committee as well as NSERC Canada external reviewer and graduate coordinator at the University of Northern British Columbia. Professor Vinogradov is advisor to Actuarial Science and Mathematical Statistics majors.

• 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