The almost sure Skorokhod representation for subsequences in nonmetric spaces

Theory of Probability and its Applications

Volumn 42, Issue 1, 1997, Pages 167-174

  Jakubowski, A ^a  

^a NICOLAUS COPERNICUS UNIVERSITY   (Poland)

Author keywords

Convergence in distribution on nonmetric topological spaces; Prokhorov's theorem; The a.s. Skorokhod representation

Indexed keywords

EID: 0031329751     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0040585x97976052     Document Type: Article

References (13)

1. P. BILLINGSLEY, Weak Convergence of Measures: Applications in Probability, SIAM, Philadelphia, 1971.
2. R. M. DUDLEY, Distances of probability measures and random variables, Ann. Math. Statist., 39 (1968), pp. 1563-1572.
3. R. M. DUDLEY, An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions, Lecture Notes in Math., 1153 (1985), pp. 141-178.
4. R. ENGELKING, General Topology, Heldermann-Verlag, Berlin, 1989.
5. P. J. FERNANDEZ, Almost surely convergent versions of sequences which converge weakly, Bol. Soc. Brasil. Mat., 5 (1974), pp. 51-61.
6. X. FERNIQUE, Processus linéaires, processus généralisés, Ann. Inst. Fourier (Grenoble), 17 (1967), pp. 1-92.
7. L. LE CAM, Convergence in distribution of stochastic processes, Univ. California Publ. Statist., 2 (1957), pp. 207-236.
8. P. A. MEYER, Le théorème de continuite de P. Lévy sur les espaces nucléaires (d'aprés X. Fernique), Sém. Bourbaki, 311 (1965-66), pp. 1-14.
9. W. RUDIN, Functional Analysis, McGraw-Hill, New York, 1973.
10. H. H. SCHAEFER, Topological Vector Spaces, Springer-Verlag, Berlin, 1970.
11. A. V. SKOROKHOD, Limit theorems for stochastic processes, Theory Probab. Appl., 1 (1956), pp. 261-290.
12. W. SZCZOTKA, A note on Skorokhod representation, Bull. Polish Acad. Sci. Math., 38 (1990), pp. 35-39.
13. M. J. WICHURA, On the construction of almost uniformly convergent random variables with given weakly convergent image laws, Ann. Math. Statist., 41 (1970), pp. 284-291.