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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Bhattacharya R.N., Rao R.R. - Normal Approximation and Asymptotic Expansions |
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| Предметный указатель |
Absolutely continuous, function 263
Absolutely continuous, signed measure 269
Asymptotically best constant in Berry - Esseen theorem 110 240
Bernoulli numbers, polynomials 272
Berry - Esseen theorem 104
Borel sigma-field of a metric space 2
Boundary of a set 4
Bounded Lipschitzian distance 17
Bounded variation of a function 263
Cauchy's estimate 68 69
Cauchy's formula 28
Central limit theorem, classical 186
Central limit theorem, multidimensional 183
Characteristic function of a probability measure 42
Chebyshev's inequality, one sided 103
Closed half space 20
Continuity set 4
Convex hull of a set 23
Convex set 20
Convolution, of finite signed measures 43
Convolution, of functions 42
Covariance matrix 261
Covariance matrix, average 59
Cramer - Edgeworth polynomials 51 52
Cramer - Levy theorem 44
Cramer's condition 207
Cumulants,  46
Degenerate distribution 226
Difference operators 262
Distribution function, of a finite signed measure 54 261
Distribution function, of a random vector 262
Distribution of a random vector 261
Euler - Maclaurin sum formula, in multidimension 275
Euler - Maclaurin sum formula, in one dimension 273
Face of a polyhedron 25
Formula in lattice case 230
Fourier inversion, theorem 41
Fourier transform 40
Fourier - Stieltjes transform 42
Fundamental domain of a lattice 229
Hausdorff distance 19
Hoelder inequality, generalized 48
Hyperplane 20
Indicator function of a set 4
Induced signed measure 43
Inner product, in  40
Inner product, in  40
Lattice 224
Lattice point problem 242
| Lattice, distribution 226
Lattice, minimal 227
Lattice, random vector 226
Liapounov coefficient 59
Liapounov's central limit theorem, multidimensional extension 185
Lindeberg's central limit theorem, multidimensional extension 183
Local central limit theorem for densities 189
Local expansion, for densities 192 194
Local expansion, for the lattice case 231
Logarithm, principal branch 45
Mean central limit theorem 172
Mean of a random vector 260
Moment, 44
Moment, absolute 45
Norm, in 40
Norm, in  40
Norm, of a matrix 124
Norm, of a matrix, of a finite signed measure 3
Normal distribution 50
Normal distribution, density 50
Oscillation, average modulus of 97
Oscillation, of a function 4
Oscillation, of a function on a set 7
Parseval's relation 44
Period 227
Period lattice 228
Plancherel theorem 41
Polya's result 23
Polyhedron 25
Prokhorov distance 5
Q-continuous function 4
Riemann - Lebesgue lemma 41
Scheffe's theorem 6
Schwartz, function 265
Schwartz, space 274
Singular measure on  270
Standard normal distribution 51
Standard normalization 160
Strongly non-lattice distribution 221
Support of a (signed) measure 2
Surface, area 27
Surface, integral 27
Uniformity class, of functions 6
Uniformity class, of sets 6
Uniqueness theorem for the Fourier - Stieltjes transform 43
Variation, of a finite signed measure - positive, negative, total 2
Variation, of a function on a set 263
Weak, convergence 3
Weak, topology 3
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