Paulauskas, V.; Stieve, Ch. On the central limit theorem in D[0,1] and D([0,1],H). (English) Zbl 0722.60023 Lith. Math. J. 30, No. 3, 267-276 (1990) and Lit. Mat. Sb. 30, No. 3, 567-579 (1990). See the review in Zbl 0709.60017. Cited in 1 ReviewCited in 8 Documents MSC: 60F05 Central limit and other weak theorems 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) Keywords:Skorokhod topology; weak convergence; rate of convergence; central limit theorem; central limit theorem for processes with values in a separable Hilbert space Citations:Zbl 0657.60011; Zbl 0709.60017 PDFBibTeX XMLCite \textit{V. Paulauskas} and \textit{Ch. Stieve}, Lith. Math. J. 30, No. 3, 267--276 (1990; Zbl 0722.60023) Full Text: DOI References: [1] P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968). · Zbl 0172.21201 [2] D. M. Cibisov, ?Some theorems on the limiting behavior of empirical distribution functions,? Selected Transl. Math. Statist. Probab.,6, 147?156 (1964). [3] S. E. Ethier and T. G. Kurtz, Markov Processes, Wiley, New York (1986). [4] M. Fisz, ?A central limit theorem for stochastic processes with independent increments,? Studia Math.,18, 223?227 (1959). · Zbl 0152.16404 [5] M. G. Hahn, ?Central limit theorem in D (0, 1),? Z. Wahrsch. verw. Geb.,44, 89?101 (1978). · Zbl 0378.60002 [6] D. Jukneviciene, ?Central limit theorem in the space D (0, 1),? Liet. Mat. Rinkinys,25, No. 3, 198?205 (1985). [7] R. Norvaisa, ?Central limit theorem for weighted martingales, with applications,? Liet. Mat. Rinkinys,29, No. 4, 754?769 (1989). [8] N. O’Reilly, ?On the convergence of empirical processes in supnorm metrics,? Ann. Probab.,2, 642?651 (1974). · Zbl 0301.60007 [9] V. Paulauskas, ?On the rate of convergence for the weighted empirical process,? Lecture Notes Math. (to be published). · Zbl 0704.60009 [10] V. Paulauskas, ?A note on the distribution of the supremum of some Gaussian processes,? The University of G?teborg, Preprint No. 13 (1988). [11] V. Paulauskas and D. Jukneviciene, ?On the rate of convergence in the central limit theorem in the space D (0, 1),? Liet. Mat. Rinkinys,28, No. 3, 507?519 (1988). [12] S. L. Phoenix and H. M. Taylor, ?The asymptotic strength distribution of a general fiber bundle,? Adv. Appl.,5, No. 2, 200?216 (1973). · Zbl 0272.60006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.