메뉴 건너뛰기




Volumn 27, Issue 3, 1999, Pages 1556-1578

Approximation, metric entropy and small ball estimates for Gaussian measures

Author keywords

Approximation number; Gaussian process; Metric entropy; Small deviation

Indexed keywords


EID: 0033164054     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (179)

References (31)
  • 1
    • 84968476146 scopus 로고
    • The integral of symmetric unimodular functions over a symmetric convex set and some probability inequalities
    • ANDERSON, T. W. (1955). The integral of symmetric unimodular functions over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6 170-176.
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 170-176
    • Anderson, T.W.1
  • 2
    • 0001668127 scopus 로고    scopus 로고
    • Estimates of entropy numbers and Gaussian measures for classes of function with bounded mixed derivative
    • BELINSKY, E. S (1998). Estimates of entropy numbers and Gaussian measures for classes of function with bounded mixed derivative. J. Approx. Theory 93 114-127.
    • (1998) J. Approx. Theory , vol.93 , pp. 114-127
    • Belinsky, E.S.1
  • 5
    • 0000261110 scopus 로고    scopus 로고
    • Metric entropy of convex hull in Banach spaces
    • To appear
    • CARL, B., KYREZI, I. and PAJOR, A., (1997). Metric entropy of convex hull in Banach spaces. J. London Math. Soc. To appear.
    • (1997) J. London Math. Soc.
    • Carl, B.1    Kyrezi, I.2    Pajor, A.3
  • 7
    • 0000660999 scopus 로고
    • The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
    • DUDLEY, R. M. (1967). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1 290-330.
    • (1967) J. Funct. Anal. , vol.1 , pp. 290-330
    • Dudley, R.M.1
  • 8
    • 0009295656 scopus 로고    scopus 로고
    • Estimatse for the small ball probabilities of the fractional Brownian sheet
    • To appear
    • DUNKER, T., (1998). Estimatse for the small ball probabilities of the fractional Brownian sheet. J. Theoret. Probab. To appear.
    • (1998) J. Theoret. Probab.
    • Dunker, T.1
  • 9
    • 0031996159 scopus 로고    scopus 로고
    • Metric entropy of integration operator and small ball probabilities of the Brownian sheet
    • DUNKER, T., KÜHN, T., LIFSHITS, M. A. and LINDE, W. (1998). Metric entropy of integration operator and small ball probabilities of the Brownian sheet. C. R. Acad. Sci. Paris 326 347-352.
    • (1998) C. R. Acad. Sci. Paris , vol.326 , pp. 347-352
    • Dunker, T.1    Kühn, T.2    Lifshits, M.A.3    Linde, W.4
  • 11
    • 0009158389 scopus 로고
    • Some probability and entropy estimates for Gaussian measures
    • GOODMAN, V. (1990). Some probability and entropy estimates for Gaussian measures. In Progr. Probab. 20 150-156.
    • (1990) Progr. Probab. , vol.20 , pp. 150-156
    • Goodman, V.1
  • 13
    • 22444455671 scopus 로고    scopus 로고
    • Chung's law for integrated Brownian motion
    • KHOSHNEVISAN, D. and SHI, Z. (1998). Chung's law for integrated Brownian motion. Trans. Amer. Math. Soc. 350 4253-4264.
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 4253-4264
    • Khoshnevisan, D.1    Shi, Z.2
  • 14
    • 0001545384 scopus 로고
    • A strong convergence theorem for Banach space valued random variable
    • KUELBS, J. (1976). A strong convergence theorem for Banach space valued random variable. Ann. Probab. 4 744-771.
    • (1976) Ann. Probab. , vol.4 , pp. 744-771
    • Kuelbs, J.1
  • 15
    • 0001461506 scopus 로고
    • Metric entropy and the small ball problem for Gaussian measures
    • KUELBS, J. and LI, W. V. (1993). Metric entropy and the small ball problem for Gaussian measures. J. Funct. Anal. 116 133-157.
    • (1993) J. Funct. Anal. , vol.116 , pp. 133-157
    • Kuelbs, J.1    Li, W.V.2
  • 19
    • 0009158390 scopus 로고    scopus 로고
    • Small deviations for Gaussian Markov processes under the sup-norm
    • To appear
    • LI, W. V. (1998) Small deviations for Gaussian Markov processes under the sup-norm. J. Theoret. Probab. To appear.
    • (1998) J. Theoret. Probab.
    • Li, W.V.1
  • 20
    • 0032092875 scopus 로고    scopus 로고
    • Existence of small ball constants for fractional Brownian motion
    • LI, W. V. and LINDE, W. (1998). Existence of small ball constants for fractional Brownian motion. C. R. Acad. Sci. Paris 326 1329-1334.
    • (1998) C. R. Acad. Sci. Paris , vol.326 , pp. 1329-1334
    • Li, W.V.1    Linde, W.2
  • 21
    • 0001077456 scopus 로고
    • Mappings of Gaussian measures in Banach spaces
    • LINDE, W. and PIETSCH, A. (1974). Mappings of Gaussian measures in Banach spaces. Theoret. Probab. Appl. 19 445-460.
    • (1974) Theoret. Probab. Appl. , vol.19 , pp. 445-460
    • Linde, W.1    Pietsch, A.2
  • 22
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • MANDELBROT, B. B. and VAN NESS, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Review 10 422-437.
    • (1968) SIAM Review , vol.10 , pp. 422-437
    • Mandelbrot, B.B.1    Van Ness, J.W.2
  • 23
    • 21844523956 scopus 로고
    • Small values of Gaussian processes and functional laws of the iterated logarithm
    • MONRAD, D. and ROOTZÉN, H. (1995). Small values of Gaussian processes and functional laws of the iterated logarithm. Probab. Theory Related Fields 101 173-192.
    • (1995) Probab. Theory Related Fields , vol.101 , pp. 173-192
    • Monrad, D.1    Rootzén, H.2
  • 24
    • 0001380430 scopus 로고
    • Remarques sur les nombres d'entropie d'un opérateur et de son transposé
    • PAJOR, A. and TOMCZAK-JAEGERMANN, N. (1985). Remarques sur les nombres d'entropie d'un opérateur et de son transposé. C. R. Acad. Sci. Paris 301 743-746.
    • (1985) C. R. Acad. Sci. Paris , vol.301 , pp. 743-746
    • Pajor, A.1    Tomczak-Jaegermann, N.2
  • 27
    • 22044451709 scopus 로고
    • On the Gaussian measure of the intersection
    • SCHECHTMAN, G., SCHLUMPRECHT, T. and ZINN, J. (1989). On the Gaussian measure of the intersection. Ann. Probab. 26 346-357.
    • (1989) Ann. Probab. , vol.26 , pp. 346-357
    • Schechtman, G.1    Schlumprecht, T.2    Zinn, J.3
  • 28
    • 0000461652 scopus 로고
    • A note on small ball probability of Gaussian processes with stationary increments
    • SHAO, Q. M. (1993). A note on small ball probability of Gaussian processes with stationary increments. J. Theoret. Probab. 6 595-602.
    • (1993) J. Theoret. Probab. , vol.6 , pp. 595-602
    • Shao, Q.M.1
  • 29
    • 0000819460 scopus 로고
    • New Gaussian estimates for enlarged balls
    • TALAGRAND, M. (1993). New Gaussian estimates for enlarged balls. Geom. Funct. Anal. 3 502-526.
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 502-526
    • Talagrand, M.1
  • 30
    • 0009290933 scopus 로고
    • On the order of growth of the ε-entropy of spaces of real continuous functional defined on a connected compactum
    • In Russian
    • TIMAN, A F. (1964). On the order of growth of the ε-entropy of spaces of real continuous functional defined on a connected compactum. Uspehi Mat. Nauk 19 173-177. (In Russian.)
    • (1964) Uspehi Mat. Nauk , vol.19 , pp. 173-177
    • Timan, A.F.1
  • 31
    • 0001499209 scopus 로고
    • Dualité des nombres d'entropie pour des opérateurs àvaleurs dans un espace de Hilbert
    • TOMCZAK-JAEGERMANN, N. (1987). Dualité des nombres d'entropie pour des opérateurs àvaleurs dans un espace de Hilbert. C. R. Acad. Sci. Paris 305 299-301.
    • (1987) C. R. Acad. Sci. Paris , vol.305 , pp. 299-301
    • Tomczak-Jaegermann, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.