Large-deviation theorems for sums of independent and identically distributed random vectors - Zaihraiev Oleksandr

Contents Introduction; Large-deviation theorems for heavy-tailed distributions attracted by normal law (Regularly varying absolutely continuous distributions * Theorems and corollaries * Proofs * Regularly varying lattice distributions * Theorems and corollaries * Proofs); Multivariate cc-stable distributions (Analytical properties of a-stable distributions * Asymptotic formulas for a-stable densities * Proofs * Large-deviation theorems for regularly varying absolutely continuous distributions attracted by a-stable law * Theorems and corollaries * Proofs * Large-deviation theorems for singular directions * Theorems and corollaries * Auxiliary statements * Proofs); Limit theorems under the Cramer condition (Gamma-like distributions * Abel-type theorem * Limit laws for conjugate distributions * Local limit theorems * Proofs * Compactly supported distributions * Abel-type theorem * Limit laws for conjugate distributions * Local limit theorems * Remarks and example * Proofs); Appendix A. Regularly varying functions and regularly varying distributions; Appendix B. Auxiliary result; Bibliography