Limit Theorems, Regularity and Moments for Affine-normalized Sums of Independent, Identically Distributed Random Vectors |
Common terms and phrases
a.s. n n Acosta affine-normalized assume Banach space Borel-Cantelli lemma Central Limit Theorem choose Chung cluster set compact with limits condition constant denotes Distributed Random Vectors domain of attraction eigenvalue exists exponent finite Gaussian GDNA Giné Griffin Hahn and Klass implies Invariance Principle Iterated Logarithm Jain Kuelbs and Zinn KZDT SMC L(T S L(T_S_ L(T_S_-b_ large deviation theory Lévy's lim inf max lim sup limit laws linear operators LLAK LLng LLnk Markov's inequality Math n n n n/LLn n₁ n₂ ng)/LLng norm notation operator-stable laws Ottaviani's inequality P(IT Partial Sums Pisier PONB Preprint proof Proposition proved Px+1 Random Vectors regularity relatively compact result shows stochastically compact subsequential limits Sums of Independent symmetric uniformly verw Wahrsch weakly convergent ΠΛ