This is a preview of subscription content, log in via an institution to check access.
References
N. N. Chentsov, Weak convergence of random processes with paths without discontinuities of the second kind and the so-called heuristic approach to the Kolmogorov-Smirnov type goodness-of-fit tests,Probab. Theor. Appl.,1, 155–161 (1956).
P. Billingsley,Convergence of Probability Measures, Wiley, New York (1968).
D. M. Chibisov, Some theorems on the limit behavior of empirical distribution functionProc. Steklov Inst. Math.,71, 104–112 (1964).
E. Gine and J. Zinn, Lectures on the central limit theorem for empirical processes,Lecture Notes in Math.,1221, 50–113 (1985).
M. Gsörgo and R. Norvaiša, Invariance principles in Banach function spaces, Carleton University, Ottawa (1990), 35, Preprint.
R. Dudley, An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions,Lecture Notes in Math.,1153, 141–178 (1984).
M. Bloznelis, Central limit theorem for stochastically continuous processes convergence to stable limit, Dep. of Math., Vilnius Univ. (1993), 14, Preprint 93–4.
M. Loève,Probability Theory, Springer-Verlag, Berlin, Heidelberg, New York (1977).
M. Bloznelis and V. Paulauskas, On the central limit theorem inD[0, 1],Statis. Probab. Lett. 17, 105–111 (1993).
P. H. Bezandry and X. Fernique, Sur la propriete de la limite centrale dansD[0, 1],Ann. Inst. H. Poincare,28, 31–46.
Additional information
N. G. Chebotarev Institute of Mathematics and Mechanics, Universitetskaja str. 17, 420008, Kazan, Tatarstan, Russia. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 2, pp. 171–180, April–June, 1995.
Translated by V. Paulauskas
Rights and permissions
About this article
Cite this article
Chuprunov, A.N. On convergence in distribution of empirical processes defined by independent random processes. Lith Math J 35, 136–143 (1995). https://doi.org/10.1007/BF02341491
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02341491