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Volumn 212, Issue 1, 2004, Pages 89-120

Sharp asymptotics of the Kolmogorov entropy for Gaussian measures

Author keywords

Ellipsoid; Functional quantization; Gaussian process; Metric entropy; Shannon entropy

Indexed keywords


EID: 3242658773     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.09.004     Document Type: Article
Times cited : (21)

References (24)
  • 2
    • 0004124953 scopus 로고    scopus 로고
    • Gaussian Measures
    • American Mathematical Society, Providence, RI
    • V.I. Bogachev, Gaussian Measures, American Mathematical Society, Providence, RI, 1998.
    • (1998)
    • Bogachev, V.I.1
  • 3
    • 0041891152 scopus 로고
    • Equivalence and singularity of Gaussian measures and applications
    • A.T. Bharucha-Reid (Ed.), Academic Press, New York
    • S.D. Chatterji, V. Mandrekar, Equivalence and singularity of Gaussian measures and applications, in: A.T. Bharucha-Reid (Ed.), Probabilistic Analysis and Related Topics, Vol. 1, Academic Press, New York, 1978, 169-197.
    • (1978) Probabilistic Analysis and Related Topics , vol.1 , pp. 169-197
    • Chatterji, S.D.1    Mandrekar, V.2
  • 4
    • 3042611273 scopus 로고    scopus 로고
    • Counting bits with Kolmogorov and Shannon
    • Technical Report 38 Stanford University
    • D.L. Donoho, Counting bits with Kolmogorov and Shannon, Technical Report 38, Stanford University, 2000.
    • (2000)
    • Donoho, D.L.1
  • 6
    • 38249037633 scopus 로고
    • Geometric and probabilistic estimates for entropy and approximation numbers of operators
    • Gordon Y. König H. Schutt C. Geometric and probabilistic estimates for entropy and approximation numbers of operators J. Approx. Theory 49 1987 219-239
    • (1987) J. Approx. Theory , vol.49 , pp. 219-239
    • Gordon, Y.1    König, H.2    Schutt, C.3
  • 7
    • 0003327429 scopus 로고    scopus 로고
    • Foundations of Quantization for Probability Distributions
    • Berlin: Springer
    • Graf S. Luschgy H. Foundations of Quantization for Probability Distributions Lecture Notes in Mathematics Vol. 1730 2000 Springer Berlin
    • (2000) Lecture Notes in Mathematics , vol.1730
    • Graf, S.1    Luschgy, H.2
  • 8
    • 3042561207 scopus 로고    scopus 로고
    • Functional quantization and small ball probabilities for Gaussian processes
    • To appear
    • S. Graf, H. Luschgy, G. Pagès, Functional quantization and small ball probabilities for Gaussian processes, J. Theoret. Probab. 16 (2003), to appear.
    • (2003) J. Theoret. Probab. , vol.16
    • Graf, S.1    Luschgy, H.2    Pagès, G.3
  • 12
    • 0001461506 scopus 로고
    • Metric entropy and the small ball problem for Gaussian measures
    • Kuelbs J. Li W.V. Metric entropy and the small ball problem for Gaussian measures J. Funct. Anal. 116 1993 133-157
    • (1993) J. Funct. Anal. , vol.116 , pp. 133-157
    • Kuelbs, J.1    Li, W.V.2
  • 14
    • 0037147356 scopus 로고    scopus 로고
    • Functional quantization of Gaussian processes
    • Luschgy H. Pagès G. Functional quantization of Gaussian processes J. Funct. Anal. 196 2002 486-531
    • (2002) J. Funct. Anal. , vol.196 , pp. 486-531
    • Luschgy, H.1    Pagès, G.2
  • 15
    • 3242721630 scopus 로고    scopus 로고
    • Sharp asymptotics of the functional quantization problem for Gaussian processes
    • Preprint LPMA No 752, University, Paris 6, Ann. Probab.to appear
    • H. Luschgy, G. Pagès, Sharp asymptotics of the functional quantization problem for Gaussian processes, Preprint LPMA No 752, University, Paris 6, Ann. Probab., 2003, to appear.
    • (2003)
    • Luschgy, H.1    Pagès, G.2
  • 16
    • 0002651892 scopus 로고
    • Approximate dimension and bases in nuclear spaces
    • Mityagin B.S. Approximate dimension and bases in nuclear spaces Russian Math. Surveys 16 1961 59-127
    • (1961) Russian Math. Surveys , vol.16 , pp. 59-127
    • Mityagin, B.S.1
  • 18
    • 0034562433 scopus 로고    scopus 로고
    • Integration questions related to fractional Brownian motion
    • Pipiras V. Taqqu M.S. Integration questions related to fractional Brownian motion Probab. Theory Relat. Fields 118 2000 251-291
    • (2000) Probab. Theory Relat. Fields , vol.118 , pp. 251-291
    • Pipiras, V.1    Taqqu, M.S.2
  • 19
    • 0003237499 scopus 로고    scopus 로고
    • Average-Case Analysis of Numerical Problems
    • Berlin: Springer
    • Ritter K. Average-Case Analysis of Numerical Problems Lecture Notes in Mathematics Vol. 1733 2000 Springer Berlin
    • (2000) Lecture Notes in Mathematics , vol.1733
    • Ritter, K.1
  • 20
    • 84976163902 scopus 로고
    • A note on coverings
    • Rogers C.A. A note on coverings Mathematika 4 1957 1-6
    • (1957) Mathematika , vol.4 , pp. 1-6
    • Rogers, C.A.1
  • 21
    • 84971146089 scopus 로고
    • Covering a sphere with spheres
    • Rogers C.A. Covering a sphere with spheres Mathematika 10 1963 157-164
    • (1963) Mathematika , vol.10 , pp. 157-164
    • Rogers, C.A.1
  • 22
    • 0012270057 scopus 로고
    • Some results on the asymptotic behavior of eigenvalues for a class of integral equations with translation kernel
    • Rosenblatt M. Some results on the asymptotic behavior of eigenvalues for a class of integral equations with translation kernel J. Math. Mech. 12 1963 619-628
    • (1963) J. Math. Mech. , vol.12 , pp. 619-628
    • Rosenblatt, M.1
  • 23
    • 0009613401 scopus 로고
    • An integrated fractional Fourier transform
    • Singer P. An integrated fractional Fourier transform J. Comput. Appl. Math. 54 1994 221-237
    • (1994) J. Comput. Appl. Math. , vol.54 , pp. 221-237
    • Singer, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.