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Volumn 41, Issue 1, 2004, Pages 93-107

Precise large deviations for sums of random variables with consistently varying tails

Author keywords

Consistently varying tail; Doubly stochastic process; Heavy tail; Matuszewska index; Negative association; Precise large deviations; Random sums

Indexed keywords


EID: 2442459020     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1077134670     Document Type: Article
Times cited : (102)

References (34)
  • 1
    • 0010007351 scopus 로고
    • Positive dependence in multivariate distributions
    • ALAM, K. AND SAXENA, K. M. L. (1981). Positive dependence in multivariate distributions. Commun. Statist. Theory Meth. 10, 1183-1196.
    • (1981) Commun. Statist. Theory Meth. , vol.10 , pp. 1183-1196
    • Alam, K.1    Saxena, K.M.L.2
  • 4
    • 2442513460 scopus 로고    scopus 로고
    • On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications
    • CAI, J. AND TANG, Q. (2004). On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications. J. Appl. Prob. 41, 117-130.
    • (2004) J. Appl. Prob. , vol.41 , pp. 117-130
    • Cai, J.1    Tang, Q.2
  • 5
    • 84963044008 scopus 로고
    • Intermediate regular and FI variation
    • CLINE, D. B. H. (1994). Intermediate regular and FI variation. Proc. London Math. Soc. 68, 594-616.
    • (1994) Proc. London Math. Soc. , vol.68 , pp. 594-616
    • Cline, D.B.H.1
  • 7
    • 0009231016 scopus 로고
    • Subexponentiality of the product of independent random variables
    • CLINE, D. B. H. AND SAMORODNITSKY, G. (1994). Subexponentiality of the product of independent random variables. Stoch. Process. Appl. 49, 75-98.
    • (1994) Stoch. Process. Appl. , vol.49 , pp. 75-98
    • Cline, D.B.H.1    Samorodnitsky, G.2
  • 8
    • 0036196226 scopus 로고    scopus 로고
    • Measuring the impact of dependence between claims occurrences
    • DENUIT, M., LEFÈVRE, C. AND UTEV, S. (2002). Measuring the impact of dependence between claims occurrences. Insurance Math. Econom. 30, 1-19.
    • (2002) Insurance Math. Econom. , vol.30 , pp. 1-19
    • Denuit, M.1    Lefèvre, C.2    Utev, S.3
  • 10
    • 0001039212 scopus 로고
    • Probability inequalities for sums of independent random variables
    • FUK, D. H. AND NAGAEV, S. V. (1971). Probability inequalities for sums of independent random variables. Theory Prob. Appl. 16, 660-675.
    • (1971) Theory Prob. Appl. , vol.16 , pp. 660-675
    • Fuk, D.H.1    Nagaev, S.V.2
  • 13
    • 0037758069 scopus 로고
    • A contribution to the theory of large deviations for sums of independent random variables
    • HEYDE, C. C. (1967a). A contribution to the theory of large deviations for sums of independent random variables. Z. Wahrscheinlichkeitsth. 7, 303-308.
    • (1967) Z. Wahrscheinlichkeitsth , vol.7 , pp. 303-308
    • Heyde, C.C.1
  • 14
    • 0004527181 scopus 로고
    • On large deviation problems for sums of random variables which are not attracted to the normal law
    • HEYDE, C. C. (1967b). On large deviation problems for sums of random variables which are not attracted to the normal law. Ann. Math. Statist. 38, 1575-1578.
    • (1967) Ann. Math. Statist. , vol.38 , pp. 1575-1578
    • Heyde, C.C.1
  • 15
    • 0010951765 scopus 로고
    • On large deviation probabilities in the case of attraction to a nonnormal stable law
    • HEYDE, C. C. (1968). On large deviation probabilities in the case of attraction to a nonnormal stable law. Sankhyā A 30, 253-258.
    • (1968) Sankhyā A , vol.30 , pp. 253-258
    • Heyde, C.C.1
  • 16
    • 0033140686 scopus 로고    scopus 로고
    • Asymptotic results for multiplexing subexponential on-off processes
    • JELENKOVIĆ, P. R. AND LAZAR, A. A. (1999). Asymptotic results for multiplexing subexponential on-off processes. Adv. Appl. Prob. 31, 394-421.
    • (1999) Adv. Appl. Prob. , vol.31 , pp. 394-421
    • Jelenković, P.R.1    Lazar, A.A.2
  • 17
    • 0000709793 scopus 로고
    • Negative association of random variables with applications
    • JOAG-DEV, K. AND PROSCHAN, F. (1983). Negative association of random variables with applications. Ann. Statist. 11, 286-295.
    • (1983) Ann. Statist. , vol.11 , pp. 286-295
    • Joag-Dev, K.1    Proschan, F.2
  • 18
    • 0031342881 scopus 로고    scopus 로고
    • Large deviations of heavy-tailed random sums with applications in insurance and finance
    • KLÜPPELBERG, C. AND MIKOSCH, T. (1997). Large deviations of heavy-tailed random sums with applications in insurance and finance. J. Appl. Prob. 34, 293-308.
    • (1997) J. Appl. Prob. , vol.34 , pp. 293-308
    • Klüppelberg, C.1    Mikosch, T.2
  • 19
    • 0038979606 scopus 로고    scopus 로고
    • On the convergence of distributions of generalized Cox processes to stable laws
    • KOROLEV, V. Y. (1999). On the convergence of distributions of generalized Cox processes to stable laws. Theory Prob. Appl. 43, 644-650.
    • (1999) Theory Prob. Appl. , vol.43 , pp. 644-650
    • Korolev, V.Y.1
  • 20
    • 0034747572 scopus 로고    scopus 로고
    • Asymptotic properties of the extrema of generalized Cox processes and their application to some problems in financial mathematics
    • KOROLEV, V. Y. (2001). Asymptotic properties of the extrema of generalized Cox processes and their application to some problems in financial mathematics. Theory Prob. Appl. 45, 136-147.
    • (2001) Theory Prob. Appl. , vol.45 , pp. 136-147
    • Korolev, V.Y.1
  • 22
    • 0002918670 scopus 로고    scopus 로고
    • Large deviations of heavy-tailed sums with applications in insurance
    • MIKOSCH, T. AND NAGAEV, A. V. (1998). Large deviations of heavy-tailed sums with applications in insurance. Extremes 1, 81-110.
    • (1998) Extremes , vol.1 , pp. 81-110
    • Mikosch, T.1    Nagaev, A.V.2
  • 23
    • 0002260883 scopus 로고
    • Integral limit theorems for large deviations when Cramér's condition is not fulfilled. I
    • NAGAEV, A. V. (1969a). Integral limit theorems for large deviations when Cramér's condition is not fulfilled. I. Theory Prob. Appl. 14, 51-64.
    • (1969) Theory Prob. Appl. , vol.14 , pp. 51-64
    • Nagaev, A.V.1
  • 24
    • 2442470716 scopus 로고
    • Integral limit theorems for large deviations when Cramér's condition is not fulfilled. II
    • NAGAEV, A. V. (1969a). Integral limit theorems for large deviations when Cramér's condition is not fulfilled. II. Theory Prob. Appl. 14, 193-208.
    • (1969) Theory Prob. Appl. , vol.14 , pp. 193-208
    • Nagaev, A.V.1
  • 25
    • 0002470053 scopus 로고
    • Limit theorems for large deviations when Cramér's conditions are violated
    • in Russian
    • NAGAEV, A. V. (1969b). Limit theorems for large deviations when Cramér's conditions are violated. Fiz-Mat. Nauk. 7, 17-22 (in Russian).
    • (1969) Fiz-Mat. Nauk. , vol.7 , pp. 17-22
    • Nagaev, A.V.1
  • 27
    • 0000895088 scopus 로고
    • Large deviations of sums of independent random variables
    • NAGAEV, S. V. (1979). Large deviations of sums of independent random variables. Ann. Prob. 7, 745-789.
    • (1979) Ann. Prob. , vol.7 , pp. 745-789
    • Nagaev, S.V.1
  • 28
    • 0040632822 scopus 로고
    • Probabilities of large deviations on the whole axis
    • ROZOVSKI, L. V. (1993). Probabilities of large deviations on the whole axis. Theory Prob. Appl. 38, 53-79.
    • (1993) Theory Prob. Appl. , vol.38 , pp. 53-79
    • Rozovski, L.V.1
  • 29
    • 0032523507 scopus 로고    scopus 로고
    • Ruin probabilities in perturbed risk models
    • SCHLEGEL, S. (1998). Ruin probabilities in perturbed risk models. Insurance Math. Econom. 22, 93-104.
    • (1998) Insurance Math. Econom. , vol.22 , pp. 93-104
    • Schlegel, S.1
  • 30
    • 0034559111 scopus 로고    scopus 로고
    • A comparison theorem on moment inequalities between negatively associated and independent random variables
    • SHAO, Q. M. (2000). A comparison theorem on moment inequalities between negatively associated and independent random variables. J. Theoret. Prob. 13, 343-356.
    • (2000) J. Theoret. Prob. , vol.13 , pp. 343-356
    • Shao, Q.M.1
  • 31
    • 0142056077 scopus 로고    scopus 로고
    • Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks
    • TANG, Q. AND TSITSIASHVILI, G. (2004). Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stoch. Process. Appl. 108, 299-325.
    • (2004) Stoch. Process. Appl. , vol.108 , pp. 299-325
    • Tang, Q.1    Tsitsiashvili, G.2
  • 32
    • 0036697112 scopus 로고    scopus 로고
    • A sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tails
    • TANG, Q. AND YAN, J. (2002). A sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tails. Sci. China A 45, 1006-1011.
    • (2002) Sci. China A , vol.45 , pp. 1006-1011
    • Tang, Q.1    Yan, J.2
  • 33
    • 0011956703 scopus 로고    scopus 로고
    • Large deviations for heavy-tailed random sums in compound renewal model
    • TANG, Q., SU, C., JIANG, T. AND ZHANG, J. S. (2001). Large deviations for heavy-tailed random sums in compound renewal model. Statist. Prob. Lett. 52, 91-100.
    • (2001) Statist. Prob. Lett. , vol.52 , pp. 91-100
    • Tang, Q.1    Su, C.2    Jiang, T.3    Zhang, J.S.4


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