Literature Cited
A. A. Borovkov and A. A. Mogul'skii, “Probabilities of large deviations in topological spaces. I,” Sib. Mat. Zh.,19, No. 5, 988–1004 (1978).
P. Groeneboom, J. Oosterhoff, and F. H. Ruymgaart, “Large deviation theorems for empirical probability measures,” Ann. Probab.,7, No. 4, 553–586 (1979).
J. Gärtner, “On large deviations from an invariant measure,” Teor. Veroyatn. Primen.,22, 27–42 (1977). [English translation: Theory of Probability and Its Applications,22, 24–39 (1977).]
L. V. Osipov, “Large deviation probabilities for sums of independent random vectors,” Teor. Veroyatn. Primen.,23, No. 3, 510–525 (1978). [English translation: Theory of Probability and Its Applications,23, 490–506 (1978).]
M. D. Donsker and S. R. S. Varadhan, “Asymptotic evaluation of certain Markov process expectations for large time. III,” Commun. Pure Appl. Math.,29, No. 4, 389–461 (1976).
X. Fernique, “Régularité de processus gaussiens,” Inventiones Math.,12, No. 4, 304–320 (1971).
J. Kuelbs, “Kolmogorov's law of the iterated logarithm for Banach space valued random variables,” Illinois J. Math.,21, No. 4, 784–800 (1977).
R. R. Bahadur and S. L. Zabell “Large deviations of the sample mean in general vector spaces,” Ann. Probab.,7, No. 4, 587–621 (1979).
Additional information
Mathematics Institute, Siberian Branch, Academy of Sciences of the USSR. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 5, pp. 12–26, September–October, 1980.
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Borovkov, A.A., Mogul'skii, A.A. Probabilities of large deviations in topological spaces. II. Sib Math J 21, 653–664 (1980). https://doi.org/10.1007/BF00973879
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DOI: https://doi.org/10.1007/BF00973879