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Probabilities of large deviations in topological spaces. I

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Literature Cited

  1. H. Cramér, “On a new limit theorem in probability theory,” Usp. Mat. Nauk,10, 166–184 (1944).

    Google Scholar 

  2. H. Chernoff, “A measure of asymptotic efficiency for tests of a hypothesis based on sums of observations,” Ann. Math. Statist.,23, 493–507 (1952).

    Google Scholar 

  3. A. A. Borovkov, “Boundary-value problems for random walks and large deviations in function spaces,” Teor. Veroyatn. Ee Primenen.,12, No. 4, 635–654 (1967).

    Google Scholar 

  4. A. A. Mogul'skii, “Large deviations for paths of multidimensional random walks,” Teor. Veroyatn. Ee Primenen.,21, No. 2, 309–329 (1976).

    Google Scholar 

  5. P. Bártfai, “On the multivariate Chernoff theorem,” Preprint of the Mathematical Institute, Hungarian Academy of Sciences, Budapest (1977).

    Google Scholar 

  6. R. R. Bahadur and S. L. Zabele, “Large deviation of the sample mean in general vector spaces,” Dept. of Statistics, Univ. of Chicago, Chicago (1977), Preprint.

    Google Scholar 

  7. O. E. Lanford, “Entropy and equilibrium states in classical statistical mechanics,” in: Statistical Mechanics and Mathematical Problems, Vol. 26, Springer-Verlag, New York (1971), pp. 1–113.

    Google Scholar 

  8. J. Kiefer and J. Wolfowitz, “On the deviation of the empiric distribution function of vector chance variables,” Trans. Am. Math. Soc.,87, No. 1, 173–186 (1958).

    Google Scholar 

  9. J. Kiefer, “On large deviations of the empiric distribution function of vector chance variables and the law of the iterated logarithm,” Pac. J. math.,11, No. 2, 649–660 (1961).

    Google Scholar 

  10. V. V. Yurinskii, “Exponential estimates for sums of independent, random vectors,” Doctoral Dissertation, Mat. Inst. Akad. Nauk SSSR, Moscow (1973).

    Google Scholar 

  11. I. N. Sanov, “On the probabilities of large deviations of random variables,” Mat. Sb.,42, No. 1, 11–44 (1957).

    Google Scholar 

  12. P. Groenboom, J. Oosterhoff, and F. H. Ruymgart, “Large deviation theorems for empirical probability measures,” Math. Center., Amsterdam (1976), Preprint.

    Google Scholar 

  13. A. A. Mogul'skii, “Large deviations in a sample space for sequences and processes with stationary increments,” Sib. Mat. Zh.,16, No. 2, 314–327 (1975).

    Google Scholar 

  14. A. D. Venttsel', “Coarse limit theorems on large deviations for Markov random processes. I, II,” Teor. Veroyatn. Ee Primenen,21, No. 2, 235–252; No. 3, 512–526 (1976).

    Google Scholar 

  15. S. R. S. Varadhan, “Asymptotic probabilities and differential equations,” Commun. Pure Appl. Math.,19, No. 3, 261–286 (1966).

    Google Scholar 

  16. R. R. Bahadur, “Asymptotic efficiency of tests and estimates,” Sankhya,221, 229–252 (1960).

    Google Scholar 

  17. W. Hoeffding, “Asymptotically optimal tests for multinomial distributions,” Ann. Math. Statist.,36, 369–468 (1965).

    Google Scholar 

  18. H. H. Schaefer, Topological Vector Spaces, Springer-Verlag (1971).

  19. W. Rudin, Functional Analysis, McGraw-Hill (1973).

  20. P. Billingsly, “Convergence of Probability Measures [in Russian], Nauka, Moscow, (1977).

    Google Scholar 

  21. Yu. V. Linnik, “Limit theorems for sums of independent random variables with consideration of large deviations. I,” Teor. Veroyatn. Ee Primenen.,6, No. 2, 145–163 (1961).

    Google Scholar 

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 19, No. 5, pp. 988–1004, September–October, 1978.

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Borovkov, A.A., Mogul'skii, A.A. Probabilities of large deviations in topological spaces. I. Sib Math J 19, 697–709 (1978). https://doi.org/10.1007/BF00973600

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  • DOI: https://doi.org/10.1007/BF00973600

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