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Billingsley P. — Convergence of Probability Measures
Billingsley P. — Convergence of Probability Measures

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Название: Convergence of Probability Measures

Автор: Billingsley P.

Аннотация:

A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the "industrial-strength" literature available today.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 253

Добавлена в каталог: 09.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon$-net      217
$\phi$-mixing      166
$\sigma$-compact      9
Alexandrov      16
Anderson      34
Arc sine law      80 138 194
Arzela-Ascoli theorem      55 221
Asymptotically independent increments      157
Bartozynski      48
Base for a topology      215
Bickel      108
Billingsley      16 17 150 195 208
Birkhoff      233
Birnbaum      108
Bjoersson      17
Blum      160
Borel set      3 7
Boundary      215
Brownian bridge      64
Brownian motion      4 62 154
Brownian motion process      64
Central limit theorem      42 72
Change of variable      222
Characteristic function of a probability measure      45
Characteristic function of a set      8
Chemoff      34 214
Chentsov      102 108
Chibisov      153
Ciesielski      205
Compactness      217
Complete set      217
Continued fractions      169 192 201
Continuity of sample paths      66
Continuity set of a measure      2 11
Continuity set of a random element      23
Convergence in distribution      23 24
Convergence in probability      24 26
Convergence-determining class      15
Coordinate variables, in C      60
Coordinate variables, in D      123
Cramer — Wold theorem      49
Darling      86 108
de Moivre — Laplace theorem      1 12
Determining class      15
Diagonal method      219
Diffusion      158
Diophantine approximation      193
Discontinuity of the first kind      109
Discrete set      215
Distribution function      17 22
Distribution of a random element      22
Doeblin      195
Domain of a random element      22
Donsker      6 76 108 143
Donsker's theorem      68 137
Doob      6 108 165
Dudley      16 153
Dunford      16
Dwass      214
Empirical distribution function      5 103 141
Equivalent metrics      215
Erdoes      6 76 86
Exchangeable random variables      212
Feller      52 81
Finite-dimensional distributions, in $R^{\infty}$      30
Finite-dimensional distributions, in C      30
Finite-dimensional distributions, in D      123
Finite-dimensional distributions, of random elements      40
Finite-dimensional sets, in $R^{\infty}$      19
Finite-dimensional sets, in C      19
Finite-dimensional sets, in D      121
Fortet      195
Function of a $\phi$-mixing process      182
Functional central limit theorem      72
Gauss's measure      169
Gaussian random function      64
Gikhman      16
Glivenko — Cantelli theorem      103
Gross      52
Hanson      150
Hardy      52
Helley's selection theorem      227
Hennequin      16
Ibragimov      195 208
Independence of random elements      26
Independent increments      61 154
Indicator function of a set      8
Interval in $R^{k}$      17
Invariance principle      72
Ito      67 86
k-dimensional Borel set      17
Kac      6 76 86 108 195
Kallianpur      16
Karlin      86 214
Keisler      233
Kesten      205
Khinchine      165
Kimme      142
Knight      77
Kolmogorov      6 16 76 102 103 123
Kolmogorov's existence theorem for $R^{\infty}$      228
Kolmogorov's existence theorem, the general case      230
Lamperti      61 77 150
LeCam      6 16 40 242
Levy      52 165
Liggett      214
Lindeberg — Levy case      77
Lindeberg — Levy theorem      3 45
Lindeberg's theorem      42
Linear Borel set      17
Local compactness      7
Local limit theorems      49
Lyapounov's theorem      44
Mann      34
Marginal distribution      20
Mark      86 143
Martingale      205
McKean      67 86
Measurability      222
Measurable cardinal      233
Modulus of continuity      54 220
Nonmeasurable cardinal      233
Normal distribution      24
One-sided process      168 183
Open cover      215
Oxtoby      10
Pardoner      153
Parthasarathy      16
Problem of measure      10 233
Products of metric spaces      224
Prohorov      6 16 34 40 52 61 76 77 123
Prohorov metric      238
Prohorov's theorem      37 240
Projection, from $R^{\infty}$      19
Projection, from C      19
Projection, from D      120
Pyke      108
Random element      22
Random function      4 22 57 128
Random variable      22
Random vector      22
Random walk case      77
Ranga Rao      16 17 29
Reflection principle      71
Regular measure      7
Relative compactness of measures      35 239
Renyi      28 142 150
Rosen      165 208 214
Rosenblatt      150
Rubin      34
Sampling      208
Scheffe's theorem      224
Schmid      142
Schwartz      16
Separability      215
Separable measure      234
Separable stochastic process      65 134
Sequential compactness      35 239
Shorack      108
Skorohod      6 16 22 123 142
Skorohod topology      111
Slutsky      34 102
Sphere      215
Stone      61 142
Strassen      77
Subspaces      224
Support      9
Tarski      233
Teicher      214
Tight family of measures      37 239
Tight measure      9
Tight sequence of random elements      40
Topological completeness      234
Topology of weak convergence      236
Topsoe      16 17 34 61 226
Tortrat      16
Totally bounded set      217
Trumbo      214
Two-sided process      166 182
Ulam      10
UNDER      60
Uniform integrability      32
Uniform topology, on C      54 220
Uniform topology, on D      150
Upper semicontinuity      218
Varadarajan      6 16 29 40 234 241 242
Wald      34
Weak convergence, of distribution functions      1 18
Weak convergence, of measures      2 7 16
Weyl's theorem      19 50
Wichura      214
Wiener      67
Wiener measure      4 61
Wiener path      63
Wiener process      64
Wold      52
Wright      52
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