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Some Asymptotic Results for One-Sided Large Deviation Probabilities

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Abstract

We investigate the asymptotic behavior of the sum of independent real random variables. We assume that the random variables are not identically distributed but the average of distribution functions of these random variables is equivalent to some heavy-tailed limit distribution function. An example with Pareto law as limit function is given.

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REFERENCES

  1. A. Baltrūnas, On the asymptotics of one-sided large deviation probabilities, Lith. Math. J., 35(1), 11–17 (1995).

    Google Scholar 

  2. D. H. Fuk, S. V. Nagaev, Probability inequalities for sums of independent random variables, Theory Probab. Appl., 16(4), 643–660 (1971).

    Google Scholar 

  3. C. C. Heyde, On large deviation problems for sums of random variables which are not attracted to the normal law, Ann. Math. Statist., 38, 1575–1578 (1967b).

    Google Scholar 

  4. C. C. Heyde, On large deviation probabilities in the case of attraction to a nonnormal stable law, Sankhā, 38, 253–258 (1968).

    Google Scholar 

  5. C. Klüppelberg, T. Mikosch, Large deviations of heavy-tailed random sums with applications in insurance and finance, J. Appl. Probab., 34, 293–308 (1997).

    Google Scholar 

  6. T. Mikosch, A. V. Nagaev, Large deviations of heavy-tailed sums with application in insurance, Extremes, 1(1), 811–110 (1998).

    Google Scholar 

  7. A. V. Nagaev, Integral limit theorems for large deviations when Cramer's condition is not fulfilled. I, II, Theory Probab. Appl., 14, 51–64, 193-208 (1969).

    Google Scholar 

  8. S. V. Nagaev, Large deviations for sums of independent random variables, in: Trans. Sixth Prague Conf. on Information Theory, Random Processes and Statistical Decision Functions, Academia, Prague (1973), pp. 657–674.

    Google Scholar 

  9. S. V. Nagaev, Large deviations of sums of independent random variables, Ann. Probab., 7, 745–789 (1979).

    Google Scholar 

  10. S. V. Nagaev, On the asymptotic behaviour of one-sided large deviation probabilities, Theory Probab. Appl., 26, 362–366 (1982).

    Google Scholar 

  11. V. V. Petrov, Limit Theorems for Sums of Independent Random Variables [in Russian], Nauka, Moskva (1987).

    Google Scholar 

  12. Q. Tang, C. Su, T. Jiang, J. Zhang, Large deviations for heavy-tailed random sums in compound renewal model, Statist. Probab. Lett., 52, 91–100 (2001).

    Google Scholar 

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Authors and Affiliations

  1. Vilnius University, Naugarduko 24, LT-2600, Vilnius, Lithuania

    A. Skučaitė

Authors
  1. V. Paulauskas
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  2. A. Skučaitė
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Paulauskas, V., Skučaitė, A. Some Asymptotic Results for One-Sided Large Deviation Probabilities. Lithuanian Mathematical Journal 43, 318–326 (2003). https://doi.org/10.1023/A:1026145503719

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  • DOI: https://doi.org/10.1023/A:1026145503719

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