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Petrov V.V. — Limit theorems of probability theory

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Название: Limit theorems of probability theory

Автор: Petrov V.V.

Аннотация:

This book offers a superb overview of limit theorems and probability inequalities for sums of independent random variables. Unique in its combination of both classic and recent results, the book details the many practical aspects of these important tools for solving a great variety of problems in probability and statistics. Topics include limit theorems on convergence to infinitely divisible distributions, the central limit theorem with rates of convergence, the weak and strong law of large numbers, the law of the iterated logarithm, and the many inequalities for sums of an arbitrary number random variables. Ideal as both a graduate text and a reference for seasoned mathematicians, Limit Theorems of Probability Theory brings the reader to the frontier of current research.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 292

Добавлена в каталог: 08.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\sigma$ -Algebra of events      1
Adler, A.      257 265
Alda, V.      135 265
Aldous, D.J.      227 265
Almost surely      204
Amosova, N.N.      138 265
Ananjevsky, S.M.      46—47 87 265
Andel, J.      238 265
Arak, T.V.      107 109—110 265 285
Araujo, A.      185 265
Arnold, B.C.      37 265
Attraction      106—107
Attraction, partial      107
Barbour, A.D.      184 194 197 265 272
Baum, L.E.      137—138 140 229 233 265
Baxter, G.      47 265
Beesack, P.R.      36 265
Bennett, G.      78 265
Bentkus, V.      42 266
Bergstroem, H.      107 184—185 266
Berkes, I.      227 238 256 260 266
Bernstein — Feller theorem      121
Bernstein's inequalities      58
Bernstein, S.N.      58 77 120 121 135 136 266 279
Berry — Esseen inequality      150 176 177 181 183
Berry, A.C.      150 176—177 181 183—185 191 265—266 270 272—273 277 284—285
Bestsennaya, R.V.      77 266
Bhattacharya, R.N.      42 184—185 197 266
Bickel, P.J.      80 86 266
Bikelis, A.      184—185 187 196 266
Billingsley, P.      44 266
Bingham, N.H.      106 233 255 266
Binmore, K.G.      40 266
Blum, J.R.      49 266
Boas, R.P.      39 266
Bondarko, V.M.      198 266
Book, S.A.      186 235—236 267
Borel field of events      1
Borel function      5
Borel set      1—4 43
Borel — Cantelli lemma      199—201 211 215 224 226 244—245 250
Borel — Cantelli sequence of events      238
Borel, E.      1—5 43 199—201 206 211 213 215 218 224 226 238 265 267—268 270 274 277
Borovkov, A.A.      79 267 282
Brosamler, G.A.      238 267
Brown, B.M.      38 267
Buldygin, V.V.      226 267
Bulinsky, A.V.      267
Butzer, P.L.      197 267
Cacoullos, T.      37 267
Cantelli, F.P.      199—201 206 211 213 215 218 224 226 238 267—268 270 274 277
Cauchy — Buniakowski inequality      6
Central limit theorem      118 120 142 169
Central limit theorem, global form      166 168
Central moment      6
Characteristic function      9—13
Characteristic function, Kolmogorov representation      36
Characteristic function, Levy representation      35
Characteristic function, Levy — Khintchine representation      30 99
Chatterjee, S.D.      47 227 267
Chebyshev — Hermite polynomials      171
Chebyshev's inequalities      6 7
Chebyshev's theorem      134
Chebyshev, P.L.      6 7 36 53 124 132 134 185 198 200 215 267 272—273 277 282
Chen, L.H.Y.      37 184 267 273
Chen, R.      141 267
Chernoff function      234
Chernoff, H.      37 234 267 274
Chistyakov, G.P.      192 267
Chover, J.      258 267
Chow, Y.S.      138 231—232 267
Christoph, G.      185 238 268
Chung, K.L.I.      77 226 268 276
Class L      101 110
Concentration functions      22 45 63 225
Constancy in the limit      98
Convergence in probability      20 127
Convergence in variation      44
Convergence, almost surely      204
Convergence, complete      16
Convergence, weak      16—18
Convolution      4
Cox, D.C.      82 268
Cramer's condition      8 57—58 178 181 235
Cramer's condition (C)      12 14 195—196 224—225
Cramer's series      178
Cramer, H.      8 36 40 57—58 178 181 185 195 198 224—225 235 268 270 277—278
Csaki, E.      258 268
Csoergoe, M.      226 235 238 255 268 283
Csoergoe, S.      230 235 238 268
Cumulant      11 178
Daley, D.J.      81 268
Darling, D.A.      234 268
Daugavet, A.I.      36 197 268—269
de Acosta, A.      255 269
Deheuvels, P.      235 269
Dehling, H.      238 266
density      2 3
Devroye, L.      235 269
Dharmadhikari, S.W.      83 269
distribution      2 3
Distribution function      2—4
Distribution, absolutely continuous      2
Distribution, Bernoulli      3 150
Distribution, binomial      3
Distribution, continuous      2
Distribution, degenerate      3 127
Distribution, discrete      2
Distribution, infinitely divisible      28—36 47—49 91 98—103 107
Distribution, lattice      2 12 13 15
Distribution, normal      3 29 112—113 118
Distribution, Poisson      3 29 31
Distribution, singular      2
Distribution, stable      103—105 110—111
Doeblin, W.      49 77 107 269 274
Domain of attraction      106—107
Doob, J.L.      41 80 269
Dupac, V.      238 265
Dyson, F.J.      44 269
Ebralidze, Sh.S.      79 269
Edgeworth, F.Y.      185 198 272
Egorov, V.A.      185 193 226 261—2 269
Eisenberg, B.      44 269
Elementary events      1
Elementary events, space of      1
Enger, J.      36
Erdoes — Renyi law      235
Erdoes, P.      77 137 199 226 235 267—9 275 277 283
Erickson, K.B.      231 269
Esseen's inequality      149
Esseen's theorem      142
Esseen, C.-G.      36 47 77 81—82 87 142 147 149—150 155 176—177 181 183—185 187 191 265 269 270 272—274 277 281 284—285
Etemadi, N.      226 229 270
Events      1
Events, mutually independent      4
Expectation      5
Fainleib, A.S.      184 270
Feller's theorem      120 131
Feller, W.      1 41 106 110—111 120—121 123 135 184 230 270 273 277 280 282
Fisher, A.      238 270
Fishier, R.M.      238 270
Fisz, M.      36 110 270
Frechet, M.      43 270
Friedman, N.      188 193 270
Frolov, A.N.      235 270
Fuk, D.Kh.      77—78 271
Gafurov, M.U.      141 283
Gan Shixin      44 269
Gaposhkin, V.F.      227 271
Gine, E.      185 265

Gnedenko, B.V.      1 15 25 101 105 107 110—111 134 185 271
Godwin, H.J.      36 271
Goetze, F.      197 271
Goldie, C.M.      106 233 266
Goursat, H.      170 271
Gradsteyn, I.S.      62 271
Growth point      3 12
Gruebel, R.      48 271
Gut, A.      260 271
Hahn, L.      197 267
Hajek — Renyi inequality      54
Hajek, J.      54 77 268 271
Hall, P.      40 87 139 174 184—185 190 194—198 227 238 265 268 271—272
Hardy, G.H.      272
Hartman — Wintner theorem      248 255
Hartman, P.      49 248 255 269 272
Hausdorff, F.      226 272
Heathcote, C.R.      41 272
Helly's theorem      16
Hengartner, W.      36 272
Heyde, C.C.      77 137 139 141 184—185 188—190 193 196 226—227 255 257 272
Hipp, C.      197 271-272
Ho, Soo-Tong      184 273
Hoeffding, W.      36 78 273
Hoelder's inequality      6 72
Hsu, P.L.      38 110 137 269 273
Hudson, W.N.      49 273
Ibragimov, I.A.      49 105 107—108 185—186 188 193 195—196 273
Independent events      4
Independent events, random variables      4—6
Infinite smallness      88
Infinitely divisible distributions      28—36 47—49 91 98—103 107
Infinitely often      199
Jain, N.C.      258 273
Jensen's inequality      6 66
Jesiak, B.      108 136 273 281
Jogdeo, K.      83 269
Johnson, W.B.      83 273
Karlin, S.      36 273
Katz, M.      137—138 140 184 229 231 265 273
Kawata concentration function      44—45
Kawata, T.      38—39 44—45 273
Kemperman, J.H.B.      82 268
Kendall, D.G.      281
Kesten's inequality      73 77
Kesten, H.      73 77 231 234 257 269 274 284
Khatuntseva, M.V.      198 274
Khintchine's theorem      91 134
Khintchine, A.      30 34 36 49 107 111—112 134 255 274
Kingman, J.F.C.      36 274
Kirsha, K.      42 266
Klaassen, C.A.J.      37 274
Klass, M.J.      255—256 274
Kochen, S.B.      226 274
Kolmogorov — Rogozin inequality      68 69 73 77
Kolmogorov's formula      36
Kolmogorov's formula, inequality      52 54 205
Kolmogorov's formula, metric      43
Kolmogorov's formula, spectral function      36
Kolmogorov's formula, theorem      131 239
Kolmogorov, A.N.      25 36 52 54 68—69 73 77 101 105 107 134 185 205 226 239 255 263 265 267 271 274 280—281 284
Kolodyazhny, S.F.      185 274
Komlos — Major — Tusnady approximation      236—237
Komlos, J.      227 235-237 266 268 274 284
Koopmans, L.H.      270
Kroneeker's lemma      209 212—213 249
Kruglov, V.M.      48 107 111 229 274—275
Kunisawa concentration function      45—46
Kunisawa, K.      45—47 275
Lacey, M.I.      238 275
Lai, T.L.      138 232 267—268
Lattice distribution      2 12 13 15
Laube, G.      36 275
Laue, G.      41 275
Law of Large Numbers, strong      216 228
Law of large numbers, weak      127—128 131
Law or the iterated logarithm      239 248
Lebesgue decomposition theorem      3
LeCam, L.      107 275
Leslie, J.R.      184 196 272 275
Levy — Khintchine formula      30 112
Levy — Khintchine formula, spectral function      34
Levy — Prohorov metric      44
Levy's concentration function      22 45 87
Levy's concentration function, formula      35 105
Levy's concentration function, inequality      51 219
Levy's concentration function, metric      43 111
Levy's concentration function, spectral function      35 65 103
Levy's concentration function, theorem      126
Levy, P.      22 30 34—36 40 43—45 47—49 65 77 87 99 103 105 107 111—112 120 126 134 176 219 266 269 274 275 279
Lifshits, B.A.      196 275
Lin, Z.Y.      235 275
Lindeberg condition      124—126
Lindeberg ratio      124 154 247—248
Lindeberg — Feller theorem      123
Lindeberg, J.W.      123—124 126 135 273 278 282
Linnik, Yu.V.      36 105 108 185—186 273 275
Littlewood, J.E.      272
Loeve, M.      1 36 107—108 134 228 275
Lower class      239
Lukacs, E.      1 36 41 44 275
Lyapunov's inequality      7 62 181 202
Lyapunov's theorem      126 155
Lyapunov, A.M.      7 36 62 120 126 181 184 265—266 270 275 278 285
Lynch, J.      235 275
Maejima, M.      42 189 275
Major, P.      236—238 268 274 276
Makabe, H.      40 276
Maller, R.A.      110 256 276
Manstavicius, E.      85 276
Marcinkiewicz, J.      77 82 230 255 261 276 277
Markov's theorem      134 223
Markov, A.A.      134 223
Martikainen, A.I.      226 228—229 232 234 238 255—257 262—263 276—277
Matskyavichyus, V.K.      187 277
Mean      5
Median      9 51
Mejlijson, I.      233 277
Mejzler, D.      108 277
Michel, R.      185 196 277
Mijnheer, J.L.      108 185 238 277
Mikosch, T.      234 258 277 283
Mills ratio      182
Mills, J.F.      182
Minkowski's inequality      6
Miroshnikov, A.L.      77 277
Mogyorodi, J.      82 277
moment      5
Moment, absolute      5
Moment, absolute central      6
Moment, central      6
Moment, moment generating function      8
Mori, T.F.      226 277
Nagaev, S.V.      36 77—78 185 191 226—228 271 277—278 284
Nakata, T.      185 190 193 198 272
Nikitenko, T.V.      260 278
O'Brien, G.L.      226
Ohkubo, H.      48—49 278
Osipov's theorem      158 167 173
Osipov, L.V.      158 167 173 184—185 194 275 278
Ostrovskii, I.V.      36 275
Paditz, L.      185 278
Pakshirajan, R.P.      47 267
Paulauskas, V.I.      184—186 191 278
Peter, E.      227 266
Petrov, V.V.      36—37 77 80 81 84 101 111 137 140—141 173—174 184—187 224 226 229—230 233—234 238 255 261 263—264 269 275 277—280
Philipp, W.      238 275
Pinelis, I.F.      77 278 280
Pitman, E.J.G.      39 280
Pitman, J.W.      41 272

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