Large and Moderate Deviation Limit Theorems for Arbitrary Sequences of Random Variables with Applications
Final rept. 15 May 88-15 Nov 90,
OLD DOMINION UNIV NORFOLK VA DEPT OF MATHEMATICAL SCIENCES
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In this research project we have obtained several limit theorems for arbitrary and dependent sequences of random variables. The limit theorems considered in this project fall into three categories namely, Large deviation local limit theorems, Strong large deviation theorems and Strong moderate deviation theorems. These three categories are dependent in the sense they all are subcategories of large deviation theory. The theory of large deviations and its many users are well described in the book by Ellis 1985 and the monograph by Varadhan 1984. This work generalized several classical limit theorems that were obtained in the literature for independent and identically distributed random variables. In the next three sections we outline briefly the technical details of the work done under this contract.
- Statistics and Probability