메뉴 건너뛰기




Volumn 46, Issue , 2016, Pages 57-93

Exact asymptotics for large deviation probabilities, with applications

Author keywords

Exponential probabilistic inequalities; Final zero crossing; Large deviation probabilities; Last negative sum; Last positive sum; Nonparametric bandit theory; Subexponential distributions; Superexponential distributions

Indexed keywords


EID: 84954527288     PISSN: 08848289     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Chapter
Times cited : (2)

References (46)
  • 1
    • 84968502690 scopus 로고
    • Large deviation probabilities for positive random variables
    • Andersen‚ G. R. (1970) Large deviation probabilities for positive random variables. Proc. Amer. Math. Soc. 24 382-384
    • (1970) Proc. Amer. Math. Soc. , vol.24 , pp. 382-384
    • Andersen‚, G.R.1
  • 2
    • 84954469912 scopus 로고
    • An integral limit theorem for sums of independent two-dimensional random vectors with allowance for large deviations in the case when Cramér’s condition is not satisfied
    • Russian, Fan" Uzbek. SSR‚ Tashkent
    • Anorina‚ L. A.; Nagaev‚ A. V. (1971) An integral limit theorem for sums of independent two-dimensional random vectors with allowance for large deviations in the case when Cramér’s condition is not satisfied. (Russian) Stochastic processes and related problems‚ Part 2 (Russian)‚ “Fan" Uzbek. SSR‚ Tashkent‚ 3-11
    • (1971) Stochastic Processes and Related problems‚ Part 2 (Russian) , pp. 3-11
    • Anorina‚, L.A.1    Nagaev‚, A.V.2
  • 3
    • 0040626754 scopus 로고
    • On tails and domains of attraction of stable measures in Banach spaces
    • Araujo‚ A. and Giné‚ E. (1979) On tails and domains of attraction of stable measures in Banach spaces. Trans. Amer. Math. Soc. 248‚ no. 1‚ 105-119
    • (1979) Trans. Amer. Math. Soc , vol.248 , Issue.1 , pp. 105-119
    • Araujo‚, A.1    Giné‚, E.2
  • 4
    • 0001505964 scopus 로고
    • On deviations of the sample mean
    • Bahadur‚ R.R. and Rao‚ R. Ranga. (1960) On deviations of the sample mean‚ Ann. Math. Stat.‚ 11‚ 123-142
    • (1960) Math. Stat , vol.11 , pp. 123-142
    • Bahadur‚, R.R.1    Ranga, R.R.2
  • 6
    • 0010038260 scopus 로고
    • Analysis of large deviations for boundary problems with arbitrary boundaries I‚ II
    • Borovkov‚ A.A. (1964). Analysis of large deviations for boundary problems with arbitrary boundaries I‚ II. In: Selected Translations in Math. Statistics and Probability‚ Vol.6‚ 218-256‚ 257-274
    • (1964) Selected Translations in Math. Statistics and Probability , vol.6
    • Borovkov‚, A.A.1
  • 8
    • 0000881436 scopus 로고
    • On the multidimensional central limit theorem
    • Borovkov‚ A.A. and Rogozin‚ B.A. (1965) On the multidimensional central limit theorem‚ Theory Probab. Appl.‚ 10‚ 52-62
    • (1965) Theory Probab. Appl , vol.10 , pp. 52-62
    • Borovkov‚, A.A.1    Rogozin‚, B.A.2
  • 9
    • 0039216061 scopus 로고
    • A theorem on sums of independent positive random variables and its application to branching processes
    • Chistyakov‚ V.P. (1964) A theorem on sums of independent positive random variables and its application to branching processes‚ Theory Probab. Appl.‚ 9‚ 710-718
    • (1964) Theory Probab. Appl , vol.9 , pp. 710-718
    • Chistyakov‚, V.P.1
  • 10
    • 0005473611 scopus 로고    scopus 로고
    • Large deviations techniques and applications. Second edition
    • Springer-Verlag‚ New York
    • Dembo‚ A. and Zeitouni‚ O. (1998) Large deviations techniques and applications. Second edition. Applications of Mathematics‚ 38, Springer-Verlag‚ New York.
    • (1998) Applications of Mathematics
    • Dembo‚, A.1    Zeitouni‚, O.2
  • 13
    • 25844528397 scopus 로고
    • Convergence rates related to the strong law of large numbers
    • Fill‚ J.A. (1983) Convergence rates related to the strong law of large numbers‚ Annals Probab.‚ 11‚ 123-142
    • (1983) Annals Probab , vol.11 , pp. 123-142
    • Fill‚, J.A.1
  • 14
    • 0010034675 scopus 로고
    • Probabilities of large deviations of sums of independent random variables attached to a stable law‚
    • Godovan’chuk‚ V.V. (1978) Probabilities of large deviations of sums of independent random variables attached to a stable law‚ Theory Probab. Appl. 23‚ 602-608
    • (1978) Theory Probab. Appl , pp. 602-608
    • Godovan’chuk‚, V.V.1
  • 15
    • 0001302930 scopus 로고
    • Subexponential distributions and dominated-variation tails
    • Goldie‚ C.M. (1978) Subexponential distributions and dominated-variation tails. J. Appl. Probability 15‚ no. 2‚ 440-442
    • (1978) J. Appl. Probability , vol.15 , Issue.2 , pp. 440-442
    • Goldie‚, C.M.1
  • 17
    • 0010951765 scopus 로고
    • On large deviation probabilities in the case of attraction to a non-normal stable law
    • Heyde‚ C. C. (1968) On large deviation probabilities in the case of attraction to a non-normal stable law. Ser. A 30 253-258
    • (1968) Ser. A , vol.30 , pp. 253-258
    • Heyde‚, C.C.1
  • 18
    • 84911340822 scopus 로고
    • Nonlinear renewal theory for conditional random walks
    • Hu‚ I. (1991) Nonlinear renewal theory for conditional random walks‚ Annals Probab.‚ 19‚ 401-22
    • (1991) Annals Probab , vol.19 , pp. 401-422
    • Hu‚, I.1
  • 19
    • 0040080306 scopus 로고
    • On the time and the excess of linear boundary crossing of sample sums
    • Kao‚ C-S. (1978) On the time and the excess of linear boundary crossing of sample sums‚ Annals Probab.‚ 6‚ 191-199
    • (1978) Annals Probab , vol.6 , pp. 191-199
    • Kao‚, C.-S.1
  • 20
    • 0002899547 scopus 로고
    • Asymptotically efficient adaptive allocation rules
    • Lai‚ T.L. and H. Robbins (1985) Asymptotically efficient adaptive allocation rules‚ Advances in Applied Mathematics‚ 6‚ 4-22
    • (1985) Advances in Applied Mathematics , vol.6 , pp. 4-22
    • Lai‚, T.L.1    Robbins, H.2
  • 21
    • 0012562428 scopus 로고
    • On the probability of large deviations for the sums of independent variables
    • Univ. California Press‚ Berkeley‚ Calif
    • Linnik‚ JU. V. (1961) On the probability of large deviations for the sums of independent variables. Proc. 4th Berkeley Sympos. Math. Statist. and Prob.‚ Vol. 2 pp. Univ. California Press‚ Berkeley‚ Calif. 289-306
    • (1961) Proc. 4Th Berkeley Sympos. Math. Statist. And Prob , vol.2 , pp. 289-306
    • Linnik‚, J.U.V.1
  • 22
    • 0002470053 scopus 로고
    • Limit theorems taking into account large deviations when Cramér’condition fails‚
    • Nagaev‚ A.V. (1969) Limit theorems taking into account large deviations when Cramér’condition fails‚ Izv. AN UzSSR‚ Ser. Fiz-Matem.‚ 6‚ 17-22
    • (1969) Izv. AN UzSSR‚ Ser. Fiz-Matem , vol.6 , pp. 17-22
    • Nagaev‚, A.V.1
  • 23
    • 0002260883 scopus 로고
    • Integral limit theorems taking large deviations into account when Cramér’condition does not hold‚ I‚ II‚
    • Nagaev‚ A.V. (1969) Integral limit theorems taking large deviations into account when Cramér’condition does not hold‚ I‚ II‚ Theory Probab. Appl.‚ 24‚51-64‚ 193-208
    • (1969) Theory Probab. Appl , vol.24
    • Nagaev‚, A.V.1
  • 25
    • 0007168953 scopus 로고
    • A property of sums of independent random variables
    • Russian
    • Nagaev‚ A.V. (1977) A property of sums of independent random variables. (Russian.) Teor. Verojatnost. i Primenen. 22‚ no. 2‚ 335-346
    • (1977) Teor. Verojatnost. I Primenen , vol.22 , Issue.2 , pp. 335-346
    • Nagaev‚, A.V.1
  • 29
    • 0000895088 scopus 로고
    • Large deviations of sums of independent random variables
    • Nagaev‚ S. V. (1979) Large deviations of sums of independent random variables. Ann. Probab. 7‚ no. 5‚ 745-789
    • (1979) Ann. Probab , vol.7 , Issue.5 , pp. 745-789
    • Nagaev‚, S.V.1
  • 30
    • 0040602895 scopus 로고
    • On probabilities of large deviations of sums of independent random variables‚
    • (in Russian)
    • Petrov‚ V.V. (1965) On probabilities of large deviations of sums of independent random variables‚ Teor. Veroyatnost. Primen.‚ 10‚ 310-322. (in Russian).
    • (1965) Teor. Veroyatnost. Primen , vol.10 , pp. 310-322
    • Petrov‚, V.V.1
  • 32
    • 0001872059 scopus 로고
    • A problem on large deviations in a space of trajectories
    • Pinelis‚ I.F. (1981) A problem on large deviations in a space of trajectories‚ Theory Probab. Appl. 26‚ no. 1‚ 69-84
    • (1981) Theory Probab. Appl , vol.26 , Issue.1 , pp. 69-84
    • Pinelis‚, I.F.1
  • 33
    • 0038772478 scopus 로고
    • Asymptotic equivalence of the probabilities of large deviations for sums and maximum of independent random variables
    • Russian, Trudy Inst. Mat.‚ 5‚ “Nauka" Sibirsk. Otdel.‚ Novosibirsk
    • Pinelis‚ I.F. (1985) Asymptotic equivalence of the probabilities of large deviations for sums and maximum of independent random variables. (Russian) Limit theorems of probability theory‚ 144-173‚ 176‚ Trudy Inst. Mat.‚ 5‚ “Nauka" Sibirsk. Otdel.‚ Novosibirsk.
    • (1985) ) Limit Theorems of Probability Theory
    • Pinelis‚, I.F.1
  • 34
    • 0001638327 scopus 로고
    • Optimum bounds for the distributions of martingales in Banach spaces
    • Pinelis‚ Iosif (1994) Optimum bounds for the distributions of martingales in Banach spaces. Ann. Probab. 22‚ no. 4‚ 1679-1706
    • (1994) Ann. Probab , vol.22 , Issue.4 , pp. 1679-1706
    • Iosif, P.I.1
  • 35
    • 0000631438 scopus 로고    scopus 로고
    • Remarks on inequalities for probabilities of large deviations
    • Russian
    • Pinelis‚ I. F.; Sakhanenko‚ A. I. Remarks on inequalities for probabilities of large deviations. (Russian) Theory Probab. Appl. 30‚ no. 1‚ 143-148
    • Theory Probab. Appl , vol.30 , Issue.1 , pp. 143-148
    • Pinelis‚, I.F.1    Sakhanenko‚, A.I.2
  • 36
    • 5344262755 scopus 로고
    • The time until the final zero crossing of random sums with application to nonparametric bandit theory
    • Pinelis‚ I.; Yakowitz‚ S. (1994) The time until the final zero crossing of random sums with application to nonparametric bandit theory‚ Appl. Math. Comput. 63‚ no. 2-3‚ 235-263
    • (1994) Appl. Math. Comput , vol.63 , Issue.2-3 , pp. 235-263
    • Pinelis‚, I.1    Yakowitz‚, S.2
  • 38
    • 84966203785 scopus 로고
    • Some aspects of the sequential design of experiments‚
    • Robbins‚ H.‚ (1952) Some aspects of the sequential design of experiments‚ Bull. Amer. Math. Soc. 58‚ 527-535
    • (1952) Bull. Amer. Math. Soc , vol.58 , pp. 527-535
    • Robbins‚, H.‚.1
  • 39
    • 84954503095 scopus 로고
    • On large deviation probabilities for sums of random variables which are attracted to the normal law
    • Rohatgi‚ V. K. (1973) On large deviation probabilities for sums of random variables which are attracted to the normal law. Comm. Statist. 2‚ 525-533
    • (1973) Comm. Statist , vol.2 , pp. 525-533
    • Rohatgi‚, V.K.1
  • 40
    • 34250404160 scopus 로고
    • Large deviations probabilities in the strong law of large numbers
    • Siegmund‚ D. (1975) Large deviations probabilities in the strong law of large numbers‚ Z. Wahrsch. verw. Gebiete 31‚ 107-113
    • (1975) Z. Wahrsch. Verw. Gebiete , vol.31 , pp. 107-113
    • Siegmund‚, D.1
  • 41
    • 0000837626 scopus 로고
    • The class of subexponential distributions
    • Teugels‚ J. L. (1975) The class of subexponential distributions. Ann. Probability 3‚ no. 6‚ 1000-1011
    • (1975) Ann. Probability , vol.3 , Issue.6 , pp. 1000-1011
    • Teugels‚, J.L.1
  • 42
    • 0038434591 scopus 로고
    • Theorems o large deviations in the case of a stable limit law
    • Fan‚ Tashkent, Russian
    • Tkachuk‚ S. G. (1974) Theorems o large deviations in the case of a stable limit law. In Random Process and Statistical Inference‚ no. 4‚ Fan‚ Tashkent 178-184. (In Russian)
    • (1974) Random Process and Statistical Inference , Issue.4 , pp. 178-184
    • Tkachuk‚, S.G.1
  • 43
    • 0038434591 scopus 로고
    • Theorems o large deviations in the case of distributions with regularly varying tails
    • Fan‚ Tashkent, In Russian
    • Tkachuk‚ S. G. (1975) Theorems o large deviations in the case of distributions with regularly varying tails. In Random Process and Statistical Inference‚ no. 5‚ Fan‚ Tashkent 164-174. (In Russian)
    • (1975) Random Process and Statistical Inference , Issue.5 , pp. 164-174
    • Tkachuk‚, S.G.1
  • 46
    • 53249089493 scopus 로고
    • On the asymptotic behavior of a class of infinitely divisible laws
    • Russian
    • Zolotarev‚ V. M. (1961) On the asymptotic behavior of a class of infinitely divisible laws. (Russian) Teor. Verojatnost. i Primenen. 6‚ 330-334.
    • (1961) Teor. Verojatnost. I Primenen , vol.6 , pp. 330-334
    • Zolotarev‚, V.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.