메뉴 건너뛰기




Volumn 47, Issue 6, 2006, Pages 990-1026

Integro-local and integral theorems for sums of random variables with semiexponential distributions

Author keywords

Cram r series; Cram r zone of deviations; Integro local theorem; Intermediate zone of deviations; Large deviations; Random walk; Segment of the Cram r series; Semiexponential distribution; Zone of approximation by the maximal summand

Indexed keywords


EID: 33845503684     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11202-006-0110-x     Document Type: Article
Times cited : (20)

References (36)
  • 1
    • 0034548944 scopus 로고    scopus 로고
    • Large deviation probabilities for random walks with semiexponential distributions
    • Borovkov A. A., "Large deviation probabilities for random walks with semiexponential distributions," Siberian Math. J., 41, No. 6, 1061-1093 (2000).
    • (2000) Siberian Math. J. , vol.41 , Issue.6 , pp. 1061-1093
    • Borovkov, A.A.1
  • 3
    • 0032235942 scopus 로고    scopus 로고
    • Integro-local limit theorems including large deviations for sums of random vectors. I
    • Borovkov A. A. and Mogul'skiǐ A. A., "Integro-local limit theorems including large deviations for sums of random vectors. I," Theory Probab. Appl., 43, 1-12 (1998).
    • (1998) Theory Probab. Appl. , vol.43 , pp. 1-12
    • Borovkov, A.A.1    Mogul'skiǐ, A.A.2
  • 5
    • 33845497427 scopus 로고
    • On probabilities of large deviations for sums of independent random variables
    • Osipov L. V., "On probabilities of large deviations for sums of independent random variables," Theory Probab. Appl., 17, 309-331 (1972).
    • (1972) Theory Probab. Appl. , vol.17 , pp. 309-331
    • Osipov, L.V.1
  • 6
    • 0000895088 scopus 로고
    • Large deviations for sums of independent random variables
    • Nagaev S. V., "Large deviations for sums of independent random variables," Ann. Probab., 7, No. 5, 745-789 (1979).
    • (1979) Ann. Probab. , vol.7 , Issue.5 , pp. 745-789
    • Nagaev, S.V.1
  • 7
    • 0040632822 scopus 로고
    • Probabilities of large deviations on the whole axis
    • Rozovskiǐ L. V., "Probabilities of large deviations on the whole axis," Theory Probab. Appl., 38, No. 1, 53-79 (1993).
    • (1993) Theory Probab. Appl. , vol.38 , Issue.1 , pp. 53-79
    • Rozovskiǐ, L.V.1
  • 8
    • 0000799924 scopus 로고
    • Some limit theorems for large deviations
    • Nagaev S. V., "Some limit theorems for large deviations," Theory Probab. Appl., 10, 214-235 (1965).
    • (1965) Theory Probab. Appl. , vol.10 , pp. 214-235
    • Nagaev, S.V.1
  • 9
    • 0042603655 scopus 로고
    • Limit theorems for large deviations when the Cramér condition is violated
    • Petrov V. V., "Limit theorems for large deviations when the Cramér condition is violated," Vestnik Leningrad Univ., I: No. 19, 49-68 (1963);
    • (1963) Vestnik Leningrad Univ. , vol.1 , Issue.19 , pp. 49-68
    • Petrov, V.V.1
  • 11
    • 0042603654 scopus 로고
    • Probabilities for large deviations if the Cramér condition is not satisfied
    • Wolf W., "Probabilities for large deviations if the Cramér condition is not satisfied," Math. Nachr., 70, 197-215 (1975).
    • (1975) Math. Nachr. , vol.70 , pp. 197-215
    • Wolf, W.1
  • 12
    • 0041601583 scopus 로고
    • Asymptotische entwicklungen fuer wahrscheinlichkeiten grosser abweichungen
    • Wolf W., "Asymptotische Entwicklungen fuer Wahrscheinlichkeiten grosser Abweichungen," Z. Wahrsch. Verw. Gebiete, Bd 40, 239-256 (1977).
    • (1977) Z. Wahrsch. Verw. Gebiete , vol.40 , pp. 239-256
    • Wolf, W.1
  • 14
    • 0002918670 scopus 로고    scopus 로고
    • Large deviations of heavy-tailed sums with applications in insurance
    • Mikosh T. and Nagaev A. V., "Large deviations of heavy-tailed sums with applications in insurance," Extremes, 1, No. 1, 81-110 (1998).
    • (1998) Extremes , vol.1 , Issue.1 , pp. 81-110
    • Mikosh, T.1    Nagaev, A.V.2
  • 15
    • 0002260883 scopus 로고    scopus 로고
    • Integral limit theorems taking deviations into account when Cramér's condition does not hold
    • 1
    • Nagaev A. V., "Integral limit theorems taking deviations into account when Cramér's condition does not hold," Teor. Veroyatnost. i Primenen., 14, I: No. 1, 51-64;
    • Teor. Veroyatnost. i Primenen. , vol.14 , Issue.1 , pp. 51-64
    • Nagaev, A.V.1
  • 16
  • 17
    • 0007168953 scopus 로고
    • On a property of sums of independent random variables
    • Nagaev A. V., "On a property of sums of independent random variables," Teor. Veroyatnost. i Primenen., 22, No. 2, 335-346 (1977).
    • (1977) Teor. Veroyatnost. i Primenen. , vol.22 , Issue.2 , pp. 335-346
    • Nagaev, A.V.1
  • 18
    • 0038772478 scopus 로고
    • The asymptotic equivalence of probabilities of large deviations for the sums and the maximum of independent random variables
    • (Novosibirsk), Novosibirsk
    • Pinelis I. F., "The asymptotic equivalence of probabilities of large deviations for the sums and the maximum of independent random variables," in: Trudy Inst. Mat. (Novosibirsk), Novosibirsk, 5, 1985, pp. 144-173.
    • (1985) Trudy Inst. Mat. , vol.5 , pp. 144-173
    • Pinelis, I.F.1
  • 19
    • 0042102504 scopus 로고    scopus 로고
    • Estimates for the distribution of sums and maxima of sums of random variables without the Cramér condition
    • Borovkov A. A., "Estimates for the distribution of sums and maxima of sums of random variables without the Cramér condition," Siberian Math. J., 41, No. 5, 811-848 (2000).
    • (2000) Siberian Math. J. , vol.41 , Issue.5 , pp. 811-848
    • Borovkov, A.A.1
  • 20
    • 0036348021 scopus 로고    scopus 로고
    • Large deviation probabilities for maxima of sums of independent random variables with negative mean and subexponential distribution
    • Korshunov D. A., "Large deviation probabilities for maxima of sums of independent random variables with negative mean and subexponential distribution," Theory Probab. Appl., 46, No. 2, 355-366 (2001).
    • (2001) Theory Probab. Appl. , vol.46 , Issue.2 , pp. 355-366
    • Korshunov, D.A.1
  • 21
    • 33845501110 scopus 로고    scopus 로고
    • The Cramér approximation with Cramér's condition violated
    • Aleshkyavichene A. K., "The Cramér approximation with Cramér's condition violated," Liet. Mat. Rink., 45, No. 4, 447-456 (2005).
    • (2005) Liet. Mat. Rink. , vol.45 , Issue.4 , pp. 447-456
    • Aleshkyavichene, A.K.1
  • 22
    • 0042603649 scopus 로고
    • On the probabilities of large deviations for the maximum of sums of independent random variables
    • 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).
    • (1979) Teor. Veroyatnost. i Primenen. , vol.24 , Issue.1 , pp. 322-337
    • Aleshkyavichene, A.K.1
  • 23
    • 0000577557 scopus 로고
    • On local and ratio limit theorems
    • Univ. California Press, Berkeley and Los Angeles
    • Stone C., "On local and ratio limit theorems," in: Proc. of the Fifth Berkeley Sympos. on Mathematical Statistics and Probability. Vol. II, part II, Univ. California Press, Berkeley and Los Angeles, 1966, pp. 217-224.
    • (1966) Proc. of the Fifth Berkeley Sympos. on Mathematical Statistics and Probability , vol.2 , Issue.PART II , pp. 217-224
    • Stone, C.1
  • 24
    • 0000983367 scopus 로고
    • A local limit theorem for nonlattice multi-dimensional distribution functions
    • Stone C., "A local limit theorem for nonlattice multi-dimensional distribution functions," Ann. Math. Statist., 36, 546-551 (1965).
    • (1965) Ann. Math. Statist. , vol.36 , pp. 546-551
    • Stone, C.1
  • 25
    • 33646004908 scopus 로고    scopus 로고
    • Integro-local theorems for sums of random vectors in a series scheme
    • Borovkov A. A. and Mogul'skiǐ A. A., "Integro-local theorems for sums of random vectors in a series scheme," Mat. Zametki, 79, No. 4, 468-482 (2006).
    • (2006) Mat. Zametki , vol.79 , Issue.4 , pp. 468-482
    • Borovkov, A.A.1    Mogul'skiǐ, A.A.2
  • 26
    • 0009966939 scopus 로고
    • Probabilities of large deviations of sums of independent random variables with a common distribution function that belongs to the domain of attraction of a normal law
    • Rozovskiǐ L. V., "Probabilities of large deviations of sums of independent random variables with a common distribution function that belongs to the domain of attraction of a normal law," Theory Probab. Appl., 34, No. 4, 625-644 (1989).
    • (1989) Theory Probab. Appl. , vol.34 , Issue.4 , pp. 625-644
    • Rozovskiǐ, L.V.1
  • 27
    • 0001872059 scopus 로고
    • A problem on large deviations in a space of trajectories
    • Pinelis I. F., "A problem on large deviations in a space of trajectories," Theory Probab. Appl., 26, 69-84 (1981).
    • (1981) Theory Probab. Appl. , vol.26 , pp. 69-84
    • Pinelis, I.F.1
  • 28
    • 0040032361 scopus 로고
    • A local limit theorem
    • Shepp L. A., "A local limit theorem," Ann. Math. Statist., 35, 419-423 (1964).
    • (1964) Ann. Math. Statist. , vol.35 , pp. 419-423
    • Shepp, L.A.1
  • 29
    • 0036439136 scopus 로고    scopus 로고
    • On subexponential distributions and asymptotics of the distribution of the maximum of sequential sums
    • Borovkov A.A., "On subexponential distributions and asymptotics of the distribution of the maximum of sequential sums," Siberian Math. J., 43, No. 6, 995-1022 (2002).
    • (2002) Siberian Math. J. , vol.43 , Issue.6 , pp. 995-1022
    • Borovkov, A.A.1
  • 30
    • 33845504610 scopus 로고    scopus 로고
    • Large deviations and super large deviations of the sums of independent random variables with the Cramér condition. I
    • Borovkov A. A. and Mogul'skiǐ A. A., "Large deviations and super large deviations of the sums of independent random variables with the Cramér condition. I," Teor. Veroyatnost. i Primenen., 51, No. 2, 260-294 (2006).
    • (2006) Teor. Veroyatnost. i Primenen. , vol.51 , Issue.2 , pp. 260-294
    • Borovkov, A.A.1    Mogul'skiǐ, A.A.2
  • 31
    • 33845496434 scopus 로고    scopus 로고
    • Large deviations and super large deviations of the sums of independent random variables with the Cramér condition. II
    • Borovkov A. A. and Mogul'skiǐ A. A., "Large deviations and super large deviations of the sums of independent random variables with the Cramér condition. II," Teor. Veroyatnost. i Primenen., 51, No. 4 (2006).
    • (2006) Teor. Veroyatnost. i Primenen. , vol.51 , Issue.4
    • Borovkov, A.A.1    Mogul'skiǐ, A.A.2
  • 32
    • 0010793190 scopus 로고
    • On a local limit theorem of probability
    • Gnedenko B. D., "On a local limit theorem of probability," Uspekhi Mat. Nauk, 3, No. 3, 187-194 (1948).
    • (1948) Uspekhi Mat. Nauk , vol.3 , Issue.3 , pp. 187-194
    • Gnedenko, B.D.1
  • 34
    • 0001618530 scopus 로고
    • On domains of attraction of multidimensional distributions
    • Rvacheva E. L., "On domains of attraction of multidimensional distributions," Uchenye Zapiski L'vov Univ. Ser. Mekh.-Mat., 6, 5-44 (1958).
    • (1958) Uchenye Zapiski L'vov Univ. Ser. Mekh.-Mat. , vol.6 , pp. 5-44
    • Rvacheva, E.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.