On the Almost Sure Limit Theorems I.A.Ibragimov, M.A. Lifshits Starting from a sequence of random vectors {zk } one can construct empirical distributions n 1 X −1 Qn = k δzk . ln n k=1
The statements about the convergence of these or similar distributions with probability one to a limit distribution are called almost sure limit theorems. We suggest several methods which admit easily deduce almost sure limit theorems from classical limit theorems, prove almost sure invariance principles, investigate the convergence of generalized moments. Our methods work not only in the case of normal limit law but also for the limit laws of general type.
On the Almost Sure Limit Theorems IAIbragimov, MA ...
The statements about the convergence of these or similar distributions with probability one to a limit distribution are called almost sure limit theorems. We.
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Let Sk be the k-th partial sum of real valued i.i.d. random variables X1,X2, ... Define the empirical measures with logarithmic weights. Qn = 1 log n. ân k=1. 1.
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Page 1. Convergence of Generalized Moments in Almost Sure. Limit Theorems. I.A.Ibragimov, M.A. Lifshits. We consider convergence of the generalized moments in the classical almost sure central limit theorem for i.i.d. square integrable random variabl
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[1] R.W. Barnard, C.H. FitzGerald, S. Gong, A distortion theorem for biholo- morphic mappings in C2, Trans. Amer. Math. Soc. 344 (1994) 907â924. [2] C.-H. Chu, H. Hamada, T. Honda, G. Kohr, Distortion theorems for convex mappings on homogeneous bal
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