References
Ibragimov I. A. and Linnik Yu. V., Independent and Stationarily Connected Variables [in Russian], Nauka, Moscow (1965).
Nagaev S. V., “Some limit theorems for large deviations,” Teor. Veroyatnost. i Primenen., 10, No. 2, 231–254 (1965).
Petrov V. V., “Limit theorems for large deviations when the Cramer condition is violated. I. II,” Vestnik Leningrad Univ., I: 19, 49–68 (1963); II: 1, 58–75 (1969).
Wolf W., “ Large deviation probabilities when the Cramer condition is violated,” Math. Nachr., Bd 70, 197–215 (1975).
Wolf W., “Asymptotische Entwicklungen fuer Wahrscheinlichkeiten grosser Abweichungen,” Z. Wahrsch. Verw. Geb., Bd 40, 239–256 (1977).
Saulis L. and Statulyavichus V., Limit Theorems for Large Deviations [in Russian], Mokslas, A'zenberg (1989).
Osipov L. V., “On large deviation probabilities for sums of independent random variables,” Teor. Veroyatnost. i Primenen., 17, No. 2, 320–341 (1972).
Aleshkyavichene A. K., “On the probabilities of large deviations for the maximum of sums of independent random variables,” Teor. Veroyatnost. i Primenen., 24, No. 1, 322–337 (1979).
Nagaev A. V., “On a property of sums of independent random variables,” Teor. Veroyatnost. i Primenen., 22, No. 2, 335–346 (1977).
Rozovskii L. V., “Probabilities of large deviations on the whole axis,” Teor. Veroyatnost. i Primenen., 38, No. 1, 53–79 (1993).
Pinelis I. F., “On asymptotic equivalence of large deviation probabilities for the sum and maximum of independent random variables,” in: Trudy Inst. Mat. (Novosibirsk), Novosibirsk, 5, 1985, pp. 144–173.
Borovkov A. A., “Estimates for the distribution of sums and maxima of sums of random variables without the Cramer condition,” Sibirsk. Mat. Zh., 41, No. 5, 997–1038 (2000).
Mikosh T. and Nagaev A. V., “Large deviations of heavy-tailed sums with applications in insurance,” Extremes, 1, No. 1, 81–110 (1998).
Nagaev A. V., “Integral limit theorems taking deviations into account when Cramer's condition does not hold,” Teor. Veroyatnost. i Primenen., 14, No. 1, 51–64 (1969).
Korshunov D. A., “Large deviation probabilities of the maximum of sums of independent random variables with negative mean and exponential distribution,” Teor. Veroyatnost. i Primenen. (to appear).
Veraverbeke N., “Asymptotic behaviour of Wiener–Hopf factors of a random walk,” Stochastic Process. Appl., 5, No. 1, 27–37 (1977).
Borovkov A. A. and Borovkov K. A., “Large deviation probabilities for random walks with a regular distribution of jumps,” Dokl. Akad. Nauk, 371, No. 1, 14–16 (2000).
Borovkov A. A. and Borovkov K. A., On Large Deviation Probabilities for Random Walks. I. Regularly Varying Distribution Tails. II. Regular Exponential Tails [in Russian] [Preprint, No. 62], Sobolev Inst. Mat., Novosibirsk (1999).
Borovkov A. A. and Boxma O. J., On Large Deviation Probabilities for Random Walks with Heavy Tails [Preprint EURANDOM], Eindhoven (2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Borovkov, A.A. Large Deviation Probabilities for Random Walks with Semiexponential Distributions. Siberian Mathematical Journal 41, 1061–1093 (2000). https://doi.org/10.1023/A:1004864002443
Issue Date:
DOI: https://doi.org/10.1023/A:1004864002443