Estimates for interval probabilities of the sums of random variables with locally subexponential distributions

Siberian Mathematical Journal

Volumn 47, Issue 4, 2006, Pages 779-786

  Shneer, V V ^a,b  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Estimates for interval probabilities; Locally subexponential distribution; Subexponential distribution; Sums of random variables

Indexed keywords

EID: 33746434021     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11202-006-0088-4     Document Type: Article

References (8)

1. Athreya K. B. and Ney P. E., Branching Processes, Springer-Verlag, Berlin (1972).
2. Shneer V. V., "Estimates for the distributions of the sums of subexponential random variables," Siberian Math. J., 45, No. 6, 1143-1158 (2004).
3. Asmussen S., Foss S., and Korshunov D., "Asymptotics for sums of random variables with local subexponential behaviour," J. Theory Probab., 16, No. 2, 489-518 (2003).
4. Borovkov A.A., "Integro-local and integral limit theorems on the large deviations of sums of random vectors: Regular distributions," Siberian Math. J., 43, No. 3, 402-417 (2002).
5. Bingham N. H., Goldie C. M., and Teugels J. L., Regular Variation, Cambridge Univ. Press, Cambridge (1989).
6. Chistyakov V. P., "A theorem on sums of independent positive random variables and its applications to branching random processes," Teor. Veroyatnost. i Primenen., 9, No. 4, 710-718 (1964).
7. Nagaev A. V., "On a property of sums of independent random variables," Teor. Veroyatnost. i Primenen., 22, No. 2, 335-346 (1977).
8. Embrechts P., Klüppelberg C., and Mikosch T., Modelling Extremal Events, Springer-Verlag, Berlin (1997).