Literature Cited
P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).
D. M. Cibisov, “Some theorems on the limiting behavior of empirical distribution functions,” Selected Transl. Math. Statist. Probab.,6, 147–156 (1964).
S. E. Ethier and T. G. Kurtz, Markov Processes, Wiley, New York (1986).
M. Fisz, “A central limit theorem for stochastic processes with independent increments,” Studia Math.,18, 223–227 (1959).
M. G. Hahn, “Central limit theorem in D (0, 1),” Z. Wahrsch. verw. Geb.,44, 89–101 (1978).
D. Jukneviciene, “Central limit theorem in the space D (0, 1),” Liet. Mat. Rinkinys,25, No. 3, 198–205 (1985).
R. Norvaisa, “Central limit theorem for weighted martingales, with applications,” Liet. Mat. Rinkinys,29, No. 4, 754–769 (1989).
N. O'Reilly, “On the convergence of empirical processes in supnorm metrics,” Ann. Probab.,2, 642–651 (1974).
V. Paulauskas, “On the rate of convergence for the weighted empirical process,” Lecture Notes Math. (to be published).
V. Paulauskas, “A note on the distribution of the supremum of some Gaussian processes,” The University of Göteborg, Preprint No. 13 (1988).
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).
S. L. Phoenix and H. M. Taylor, “The asymptotic strength distribution of a general fiber bundle,” Adv. Appl.,5, No. 2, 200–216 (1973).
Additional information
Vilnius University. Friedrich-Schiller Universitat, Jena, German Democratic Republic. Trnaslated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 30, No. 3, pp. 567–579, July–September, 1990.
Rights and permissions
About this article
Cite this article
Paulauskas, V., Stieve, C. On the central limit theorem in D[0, 1] and D([0, 1], H). Lith Math J 30, 267–276 (1990). https://doi.org/10.1007/BF00970810
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970810