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Borovskikh Y.V. — Random permanents
Borovskikh Y.V. — Random permanents



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Название: Random permanents

Автор: Borovskikh Y.V.

Аннотация:

The determination of permanent random measures and the representation of symmetric statistics as functionals of symmetrization random measures with some deterministic kernels, make it possible to clarify the influence of properties of a random measure on the limiting results for symmetric statistics and also to study the influence of the characteristic structure of the kernels. This approach in the theory of symmetric statistics has inspired the authors to investigate random permanents and their generating functions in detail. New limiting results for random permanents are basically obtained by employing the algebraic and analytical properties of the permanents of sampling matrices and their generating functions. This motion allows clarification of different schemes in the asymptotic analysis of symmetric statistics as the size of a sample n tends to infinity. The book should be of interest to specialists working on theory and applications in the field of probability theory and statistical analysis.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 194

Добавлена в каталог: 23.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\delta$-measure      27 125 126
Asymptotic analysis      3 6 61
Asymptotic behaviour      88 136
Asymptotic behaviour of permanent      61
Asymptotic estimate      72 84 128
Asymptotic expansion      77
Asymptotic normality      176
Asymptotic property      126
asymptotic relations      149
Asymptotic representation      54 63 64 141 142 146 148 149
Asymptotic representation of the coefficient      87
Bernoulli random element      64 65
Bernoulli random variable      25 27 61
Bernoulli sample      45 46 63
Bernoulli scheme      61
Bootstrap, permanent      172
Bootstrap, permanent measure      173
Bootstrap, permanent sample      172
Bootstrap, sample      6 172 173
Bootstrap, sampling function      172
Bootstrap, symmetric statistics      173
Bootstrap, variable      167 175
Cauchy formula      17—19 42 78
Cauchy integral      42 80
Centered Poisson measure      29 36 37 118
Centered random $\delta$-measure      31
Central limit theorem      122 147 178
Characteristic function      107 108 132 133
Charlier representation      36
Charlier stochastic polynomial      3 105
Charlier — Poisson functional stochastic polynomials      50
Charlier — Poisson functionals with degenerate kernels      58
Charlier — Poisson polynomial      26
Charlier — Poisson stochastic polynomial      26—28 34 46 135
Composition method      106 133
Composition method, permanent variant      107
Counting measure      30 31 33 49 126
Counting measure, permanent multiple centered      31
Counting random measure      40
Covariance function      98
Decomposition      19 21 22 106
Decomposition, formula      7 10 12 19 23 27 136 137 141 146—150 153 154 158 175
Decomposition, representation      142
Degenerate kernel      24 37 101 105
Deterministic kernel      103
Dirac measure      97
Dirac permanent measure      97 98 100
Distribution function      121
Fourier coefficient      105
Fourier series      104
Frequency representation for the permanent      62
Functional sampling matrix      33 176
Functionals with shift      50
Gaussian approximation      136 157
Gaussian approximation scheme      135 155
Gaussian measure      98 133
Gaussian permanent measure      98 99
Gaussian random measure      98
Gaussian random variable      158
Generating function      7 12 31 33 36—38 40 46 66 72 144 151 176
Generating function of the Appell — Wick polynomials      73
Generating function of the Hermite polynomial      65 69
Generating multiple sampling function      32 68
Generating sampling function      26 28 36 61 65 66 154
Hermite polynomial      64 136 168 171
Hoeffding decomposition formula      120 123 124 128
Ito — Poisson formula      129
Ito — Poisson integral      36 37 40
Ito — Poisson stochastic integral      24 29 126
Ito — Wiener stochastic integral      104
Kernel      37
L-statistics      176 178
Laplace decomposition formula      7 138
Laplace formula      8 9 11 22 109
Martingale difference      6 167 169 171
Martingale permanent      167
Matrix      7
Matrix algebra      3 5
Mixed approximation condition      141 152 153
Mixed sampling permanents      133
Mixture approximation condition      142
Multiple functional matrix      24 37 38
Multiple functional matrix, sampling matrix      10 11 15 19 30 31 92
Multiple functional matrix, stochastic integral      102
Multiple sample      68 77 85
Multiple sampling permanent random process      92
Normal approximation      149
Normal approximation, condition      147 152
Order permanent      176
Permanent      5 7 9 19 24 31 39 40 56 111 137
Permanent as a Cauchy integral representation      80
Permanent of multiple sampling matrix      78 80
Permanent of sampling matrix      28
Permanent, approach      176
Permanent, counting measure      27 28 38
Permanent, functional      33 35
Permanent, functional, with shift      54
Permanent, generating function      46
Permanent, measure      129 176
Permanent, multiple counting measure      29 30
Permanent, multiple functional      36 38 39 58
Permanent, multiple sampling      77
Permanent, normalised      64
Permanent, random, $\delta$-measure      126
Permanent, random, measure      3 5 97 100 102 176
Permanent, symmetric, statistics      97 100 102 107 176
Permanent, with shift      45 51
poisson      25 40
Poisson, approximation      155
Poisson, approximation, condition      26 28 31 34 38 39 45 46 49 105 119 135 144 147 149 152 156
Poisson, approximation, scheme      24 25 28 31 32 51 119 126 127 135 155 156
Poisson, approximation, weak convergence      45
Poisson, centered measure      36
Poisson, law      100
Poisson, measure      37 41 126
Poisson, permanent measure      100
Poisson, random measure      28 40 49 100 118 129
Poisson, random variable      135
Poisson, stochastic integral      104 105
Primitive kernel      121 128
Radon finite measure      152
Radon measure      27 49 126
Random $\delta$-measure      30
Random Bernoulli variable      25 27
Random element      24
random matrix      132
Random measure, Gaussian      107
Random measure, infinitely divisible      107
Random measure, Poisson      107
Random permanent      3 6 25 26 28 58 177 178
Random permanent, measure      132
Random variable      25 27 40 42 61
Random variable, centered      28
Rate of convergence      155 156 158
Representation of Appell — Wick polynomials      73
Representation of coefficient      87
Representation of frequencies      63
Representation of generating function      31 34 37 176
Representation of generating sampling function      27 65
Representation of Ito — Poisson stochastic integral      29
Representation of permanent      20 40 76 80 86 138 141
Representation of permanent measure      30 99
Representation of permanent of the mixed matrix      140
Representation of sample      141
Representation of sampling function      173
Representation of sampling matrix      64
Representation of symmetric statistics      3 6 100 101 105
Representation of the moment of permanent      99
Representation of the permanent of matrix      46
Representation of the permanent process      92
Representation of U-statistics      3 122 127
Sampling with Bernoulli random elements      64
Sampling with replacement      172
Sampling, accumulated frequencies      62
Sampling, functional matrix      33 40
Sampling, matrix      7 10 25 28 51 135—137 140 157 167
Sampling, permanent      75 167
Shift      50
Shift, centered      49
Shift, decomposition      16 18 20
Shift, decomposition formula      32 35 39 55
Shift, decomposition of permanent      16 19
Simple sample      27 83 97
Simple sampling      5
Stable, approximation scheme      42 58 131
Stable, distribution      42 132
Stable, law      42
Stable, measure      133
Stable, random variable      42 43
Standard Wiener process      95
Statistical image      24 27 35 37 46 50 102 105
Statistical image of Appell — Wick polynomials      80
Statistical image of the Hermite polynomial      65
Statistical image of the Ito — Poisson stochastic integral      39
Stochastic Charlier polynomial      105
Stochastic Charlier — Poisson polynomial      26—28 34 135
Stochastic Ito — Poisson integral      118 119
Stochastic Kravchuk polynomial      65 63 66
Stochastic Poisson integral      105
Stochastic Wiener — Ito integral      107
Symmetric function      108 173
Symmetric kernel      39
Symmetric polynomial      5 7 42 139
Symmetric statistics      95 103—106
Theory of permanents      3 5
Theory of symmetric statistics      3
Theory of U statistics      3
U-statistics      3 5 101 115 116 120—122 124 126 127
Weak convergence      6 26 31 39 49 50 75 104—107 118 123 124 126 128 130 132 135 136 143 151 153—155 167 170 177
Weak limit      28 36 38 138
Wiener random measure      102 123
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