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Volumn 78, Issue 2, 1998, Pages 217-244

On the almost sure asymptotic behaviour of stochastic algorithms

Author keywords

60F05; 60F15; 62F12; 62L20; Law of the iterated logarithm; Quadratic strong law of large numbers; Stochastic algorithms

Indexed keywords


EID: 0001129018     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(98)00029-5     Document Type: Article
Times cited : (62)

References (27)
  • 2
    • 0000123608 scopus 로고
    • Asymptotic behavior of a class of stochastic approximation procedures
    • Berger E. Asymptotic behavior of a class of stochastic approximation procedures. Probab. Theoret. Fields. 71:1986;517-552.
    • (1986) Probab. Theoret. Fields , vol.71 , pp. 517-552
    • Berger, E.1
  • 3
    • 38249037320 scopus 로고
    • Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds
    • Chen H.F., Guo, L., Gao, A.J., 1988. Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds. Stochastic Process. Appl., 217-231.
    • (1988) Stochastic Process. Appl. , pp. 217-231
    • Chen, H.F.1    Guo, L.2    Gao, A.J.3
  • 4
    • 85033888148 scopus 로고    scopus 로고
    • Méthodes récursives aléatoires, Masson, 1990
    • Springer, Berlin.
    • Duflo, M., 1996. Méthodes récursives aléatoires, Masson, 1990. In: English Stochastic Iterative Models, Springer, Berlin.
    • (1996) In: English Stochastic Iterative Models
    • Duflo, M.1
  • 6
    • 0039042983 scopus 로고
    • Sur la loi des grands nombres pour les martingales vectorielles et I'estimateur des moindres carrés d'un modéle de régression
    • Duflo M., Sénoussi R., Touati A. Sur la loi des grands nombres pour les martingales vectorielles et I'estimateur des moindres carrés d'un modéle de régression. Ann. Inst. H. Poincaré 26:1990;549-566.
    • (1990) Ann. Inst. H. Poincaré , vol.26 , pp. 549-566
    • Duflo, M.1    Sénoussi, R.2    Touati, A.3
  • 8
    • 0001886994 scopus 로고
    • On the law of the iterated logarithm in stochastic approximation processes
    • Gaposhkin V.E., Krasulina T.P. On the law of the iterated logarithm in stochastic approximation processes. Theory Probab. Appl. 19:1974;844-850.
    • (1974) Theory Probab. Appl. , vol.19 , pp. 844-850
    • Gaposhkin, V.E.1    Krasulina, T.P.2
  • 9
    • 0028202634 scopus 로고
    • Rates of convergence for an adaptive filtering algorithm driven by stationary dependent data
    • Heunis A.J. Rates of convergence for an adaptive filtering algorithm driven by stationary dependent data. SIAM J. Control Optim. 32:1994;113-139.
    • (1994) SIAM J. Control Optim. , vol.32 , pp. 113-139
    • Heunis, A.J.1
  • 11
    • 0017836680 scopus 로고
    • Limit theorems for weighted sums and stochastic approximation processes
    • Lai T.Z., Robbins H. Limit theorems for weighted sums and stochastic approximation processes. Proc. Natl. Acad. Sci. USA. 75:1978;1068-1070.
    • (1978) Proc. Natl. Acad. Sci. USA , vol.75 , pp. 1068-1070
    • Lai, T.Z.1    Robbins, H.2
  • 12
    • 0040226900 scopus 로고
    • A note on martingale difference sequences satisfying the local Marankiewicz-Zigmund condition
    • Lai T.Z., Wei C.Z. A note on martingale difference sequences satisfying the local Marankiewicz-Zigmund condition, Bull. of the institute of mathematics. Academia Sinica. 11:1983;1-13.
    • (1983) Bull. of the Institute of Mathematics. Academia Sinica , vol.11 , pp. 1-13
    • Lai, T.Z.1    Wei, C.Z.2
  • 14
    • 0002346423 scopus 로고
    • About the averaging approach schemes for stochastic approximation
    • Le Breton, A., 1993. About the averaging approach schemes for stochastic approximation. Math. Methods Statist. 2, 295-315.
    • (1993) Math. Methods Statist. , vol.2 , pp. 295-315
    • Le Breton, A.1
  • 15
    • 0001589037 scopus 로고
    • Averaging for estimating covariances in stochastic approximation
    • Le Breton, A., Novikov, A., 1994. Averaging for estimating covariances in stochastic approximation, Math. Methods Statist. 3, 244-266.
    • (1994) Math. Methods Statist. , vol.3 , pp. 244-266
    • Le Breton, A.1    Novikov, A.2
  • 16
    • 21844517029 scopus 로고
    • Some results about averaging in stochastic approximation
    • Le Breton, A., Novikov, A., 1995. Some results about averaging in stochastic approximation. Metrika 42, 153-171.
    • (1995) Metrika , vol.42 , pp. 153-171
    • Le Breton, A.1    Novikov, A.2
  • 17
    • 0002236203 scopus 로고
    • Log-log-invarianzprinzipien für prozess der stochastischen approximation
    • Mark, G., 1982. Log-log-invarianzprinzipien für prozess der stochastischen approximation. Mitteilungen Math. Sem. Giessen, 153.
    • (1982) Mitteilungen Math. Sem. Giessen , vol.153
    • Mark, G.1
  • 18
    • 0346383183 scopus 로고
    • Stochastic approximation and recursive estimations, Nauka, Moscow, 1972
    • Amer. Math. Soc.
    • Nevelson, M.B., Has'minskii, R.Z., 1973. Stochastic approximation and recursive estimations, Nauka, Moscow, 1972. Translation of Math. Monographs, 47. Amer. Math. Soc.
    • (1973) Translation of Math. Monographs , vol.47
    • Nevelson, M.B.1    Has'Minskii, R.Z.2
  • 19
    • 0040226901 scopus 로고
    • Arithmetic means and invariance principles in stochastic approximation
    • Pechtl A. Arithmetic means and invariance principles in stochastic approximation. J. theoret. Probab. 6:1993;153-173.
    • (1993) J. Theoret. Probab. , vol.6 , pp. 153-173
    • Pechtl, A.1
  • 20
    • 0040226899 scopus 로고    scopus 로고
    • Efficacité asymptotique presque sûre des algorithmes stochastiques moyennisés
    • Pelletier M. Efficacité asymptotique presque sûre des algorithmes stochastiques moyennisés. C.R. Acad. Sci. Paris. 323:1996;813-816.
    • (1996) C.R. Acad. Sci. Paris , vol.323 , pp. 813-816
    • Pelletier, M.1
  • 22
    • 0032363716 scopus 로고    scopus 로고
    • Weak convergence rates for stochastic approximation with application to multiple targets and simulated annealing
    • Pelletier, M., 1998. Weak convergence rates for stochastic approximation with application to multiple targets and simulated annealing. Ann. Appl. Probab. 8, 10-44.
    • (1998) Ann. Appl. Probab. , vol.8 , pp. 10-44
    • Pelletier, M.1
  • 23
    • 0010921719 scopus 로고
    • Almost sure approximations to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise
    • Ruppert D. Almost sure approximations to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise. Ann. Probab. 10:1982;178-187.
    • (1982) Ann. Probab. , vol.10 , pp. 178-187
    • Ruppert, D.1
  • 25
    • 0001504983 scopus 로고
    • A martingale analogue of Kolmogorov's law of the iterated logarithm
    • Stout W.F. A martingale analogue of Kolmogorov's law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie. 15:1970;279-290.
    • (1970) Z. Wahrscheinlichkeitstheorie , vol.15 , pp. 279-290
    • Stout, W.F.1
  • 26
    • 0001195757 scopus 로고
    • Asymptotic properties of least-squares estimates in stochastic regression models
    • Wei C.Z. Asymptotic properties of least-squares estimates in stochastic regression models. Ann. Statist. 13:1985;1498-1508.
    • (1985) Ann. Statist. , vol.13 , pp. 1498-1508
    • Wei, C.Z.1
  • 27
    • 0001732503 scopus 로고
    • Adaptive prediction by least squares predictors in stochastic regression models with applications to time series
    • Wei C.Z. Adaptive prediction by least squares predictors in stochastic regression models with applications to time series. Ann. Statist. 15:1987;1667-1682.
    • (1987) Ann. Statist. , vol.15 , pp. 1667-1682
    • Wei, C.Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.