Polynomial convergence order of stochastic Bernstein approximation
Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wu, Zongmin [verfasserIn] Zhou, Xuan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Advances in computational mathematics - Bussum : Baltzer Science Publ., 1993, 46(2020), 1 vom: 10. Feb. |
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| Übergeordnetes Werk: |
volume:46 ; year:2020 ; number:1 ; day:10 ; month:02 |
| Links: |
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| DOI / URN: |
10.1007/s10444-020-09742-w |
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| Katalog-ID: |
SPR010113126 |
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| 520 | |a Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. | ||
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10.1007/s10444-020-09742-w doi (DE-627)SPR010113126 (SPR)s10444-020-09742-w-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Wu, Zongmin verfasserin aut Polynomial convergence order of stochastic Bernstein approximation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. Stochastic sampling (dpeaa)DE-He213 Bernstein polynomial (dpeaa)DE-He213 Finite difference (dpeaa)DE-He213 Higher-order moments (dpeaa)DE-He213 Polygamma function (dpeaa)DE-He213 Zhou, Xuan verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 10. Feb. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:10 month:02 https://dx.doi.org/10.1007/s10444-020-09742-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 10 02 |
| spelling |
10.1007/s10444-020-09742-w doi (DE-627)SPR010113126 (SPR)s10444-020-09742-w-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Wu, Zongmin verfasserin aut Polynomial convergence order of stochastic Bernstein approximation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. Stochastic sampling (dpeaa)DE-He213 Bernstein polynomial (dpeaa)DE-He213 Finite difference (dpeaa)DE-He213 Higher-order moments (dpeaa)DE-He213 Polygamma function (dpeaa)DE-He213 Zhou, Xuan verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 10. Feb. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:10 month:02 https://dx.doi.org/10.1007/s10444-020-09742-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 10 02 |
| allfields_unstemmed |
10.1007/s10444-020-09742-w doi (DE-627)SPR010113126 (SPR)s10444-020-09742-w-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Wu, Zongmin verfasserin aut Polynomial convergence order of stochastic Bernstein approximation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. Stochastic sampling (dpeaa)DE-He213 Bernstein polynomial (dpeaa)DE-He213 Finite difference (dpeaa)DE-He213 Higher-order moments (dpeaa)DE-He213 Polygamma function (dpeaa)DE-He213 Zhou, Xuan verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 10. Feb. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:10 month:02 https://dx.doi.org/10.1007/s10444-020-09742-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 10 02 |
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10.1007/s10444-020-09742-w doi (DE-627)SPR010113126 (SPR)s10444-020-09742-w-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Wu, Zongmin verfasserin aut Polynomial convergence order of stochastic Bernstein approximation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. Stochastic sampling (dpeaa)DE-He213 Bernstein polynomial (dpeaa)DE-He213 Finite difference (dpeaa)DE-He213 Higher-order moments (dpeaa)DE-He213 Polygamma function (dpeaa)DE-He213 Zhou, Xuan verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 10. Feb. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:10 month:02 https://dx.doi.org/10.1007/s10444-020-09742-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 10 02 |
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10.1007/s10444-020-09742-w doi (DE-627)SPR010113126 (SPR)s10444-020-09742-w-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Wu, Zongmin verfasserin aut Polynomial convergence order of stochastic Bernstein approximation 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. Stochastic sampling (dpeaa)DE-He213 Bernstein polynomial (dpeaa)DE-He213 Finite difference (dpeaa)DE-He213 Higher-order moments (dpeaa)DE-He213 Polygamma function (dpeaa)DE-He213 Zhou, Xuan verfasserin aut Enthalten in Advances in computational mathematics Bussum : Baltzer Science Publ., 1993 46(2020), 1 vom: 10. Feb. (DE-627)320506533 (DE-600)2012896-4 1572-9044 nnns volume:46 year:2020 number:1 day:10 month:02 https://dx.doi.org/10.1007/s10444-020-09742-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 46 2020 1 10 02 |
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Wu, Zongmin @@aut@@ Zhou, Xuan @@aut@@ |
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polynomial convergence order of stochastic bernstein approximation |
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Polynomial convergence order of stochastic Bernstein approximation |
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Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. |
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Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. |
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Abstract Recently, authors of Wu et al. (Adv. Comput. Math. 38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper. |
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