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The invariance principle for Banach space valued random variables. (English) Zbl 0258.60009


MSC:

60B10 Convergence of probability measures
60G15 Gaussian processes
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References:

[1] Brieman, L., (Probability (1968), Addison-Wesley: Addison-Wesley Reading, MA)
[2] Donsker, M. D., An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc., 6, 1-12 (1951) · Zbl 0042.37602
[3] Feller, W., (An Introduction to Probability Theory and Its Applications, Vol. II (1966), John Wiley and Sons: John Wiley and Sons New York) · Zbl 0138.10207
[4] Fernique, A., Intégralité des vecteurs Gaussiens, C. R. Acad. Sci. Paris, 270, 1698-1699 (1970) · Zbl 0206.19002
[5] Gnedenko, B. V., (The Theory of Probability (1962), Chelsea Publishing Company: Chelsea Publishing Company New York)
[6] Gross, L., Lectures in modern analysis and applications II, (Lecture Notes in Mathematics, Vol. 140 (1970), Springer-Verlag: Springer-Verlag New York)
[7] Gross, L., Potential theory on Hilbert space, J. Functional Analysis, 1, 123-181 (1967) · Zbl 0165.16403
[8] Kuelbs, J., The invariance principle for a lattice of random variables, Ann. Math. Statist., 39, 382-389 (1968) · Zbl 0164.46401
[9] Parthasarthy, K. R., (Probability Measures on Metric Spaces (1967), Academic Press: Academic Press New York)
[10] Prokhorov, Yu. V., Convergence of random processes and limit theorems in probability theory, Theor. Prob. Appl., 1, 157-214 (1956) · Zbl 0075.29001
[11] Wichura, M. J., Inequalities with applications to the weak convergence of random processes with multi-dimensional time parameters, Ann. Math. Statist., 40, 681-687 (1969) · Zbl 0214.17701
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