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2010 PAP, G., Central limit theorems on nilpotent Lie groups, Probab. Math. Statist. 14 (1993), 287-312. MR 96c :22010 Central limit theorems on nilpotent Lie
Bolthausen, E. , On a functional central limit theorem for random walks conditioned to stay positive, The Annals of Probability , 4 , No. 3, 480–485, 1976. Bolthausen E. On a functional
Hamana, Y. , On the central limit theorem for the multiple point range of random walk, J. Fac. Sci. Univ. Tokyo 39 (1992), 339–363. MR 93h :60112 Hamana Y. On the central
Summary
We provide uniform rates of convergence in the central limit theorem for linear negative quadrant dependent (LNQD) random
variables. Let
Fukuyama, K. , The central limit theorem for Riesz-Raikov sums, Prob. Theory Related Fields , 100 (1994), no. 1, 57–75. MR 1292190 ( 95i :60020) Fukuyama K. The central limit theorem
Zhang, L. X. , A functional central limit theorem for asymptotically negatively dependent random fields, Acta Math. Hungar. , 86 (3) (2000a), 237–259. MR 1756175 ( 2001c :60055) Zhang L. X
589 Bradley, R. C. , A central limit theorem for stationary ρ -mixing sequences with infinite variance, Ann. Probab. , 16 (1988), 313–332. MR 89a :60053
] Hall , P. , Heyde , C. C. 1980 Martingale Limit Theory and Its Applications Academic Press New York . [6] Johnson , O. , Samworth , R. 2005 Central limit theorem and convergence to
Abstract
Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put