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Petrov V.V. Ч Limit theorems of probability theory
Petrov V.V. Ч Limit theorems of probability theory

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Ќазвание: Limit theorems of probability theory

јвтор: Petrov V.V.

јннотаци€:

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.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1995

 оличество страниц: 292

ƒобавлена в каталог: 08.12.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный 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.      46Ч47 87 265
Andel, J.      238 265
Arak, T.V.      107 109Ч110 265 285
Araujo, A.      185 265
Arnold, B.C.      37 265
Attraction      106Ч107
Attraction, partial      107
Barbour, A.D.      184 194 197 265 272
Baum, L.E.      137Ч138 140 229 233 265
Baxter, G.      47 265
Beesack, P.R.      36 265
Bennett, G.      78 265
Bentkus, V.      42 266
Bergstroem, H.      107 184Ч185 266
Berkes, I.      227 238 256 260 266
Bernstein Ч Feller theorem      121
Bernstein's inequalities      58
Bernstein, S.N.      58 77 120 121 135 136 266 279
Berry Ч Esseen inequality      150 176 177 181 183
Berry, A.C.      150 176Ч177 181 183Ч185 191 265Ч266 270 272Ч273 277 284Ч285
Bestsennaya, R.V.      77 266
Bhattacharya, R.N.      42 184Ч185 197 266
Bickel, P.J.      80 86 266
Bikelis, A.      184Ч185 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 235Ч236 267
Borel field of events      1
Borel function      5
Borel set      1Ч4 43
Borel Ч Cantelli lemma      199Ч201 211 215 224 226 244Ч245 250
Borel Ч Cantelli sequence of events      238
Borel, E.      1Ч5 43 199Ч201 206 211 213 215 218 224 226 238 265 267Ч268 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.      199Ч201 206 211 213 215 218 224 226 238 267Ч268 270 274 277
Cauchy Ч Buniakowski inequality      6
Central limit theorem      118 120 142 169
Central limit theorem, global form      166 168
Central moment      6
Characteristic function      9Ч13
Characteristic function, Kolmogorov representation      36
Characteristic function, Levy representation      35
Characteristic function, Levy Ч Khintchine representation      30 99
Chatterjee, S.D.      47 227 267
Chebyshev Ч 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 272Ч273 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 231Ч232 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      16Ч18
Convolution      4
Cox, D.C.      82 268
Cramer's condition      8 57Ч58 178 181 235
Cramer's condition (C)      12 14 195Ч196 224Ч225
Cramer's series      178
Cramer, H.      8 36 40 57Ч58 178 181 185 195 198 224Ч225 235 268 270 277Ч278
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 268Ч269
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      2Ч4
Distribution, absolutely continuous      2
Distribution, Bernoulli      3 150
Distribution, binomial      3
Distribution, continuous      2
Distribution, degenerate      3 127
Distribution, discrete      2
Distribution, infinitely divisible      28Ч36 47Ч49 91 98Ч103 107
Distribution, lattice      2 12 13 15
Distribution, normal      3 29 112Ч113 118
Distribution, Poisson      3 29 31
Distribution, singular      2
Distribution, stable      103Ч105 110Ч111
Doeblin, W.      49 77 107 269 274
Domain of attraction      106Ч107
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 261Ч2 269
Eisenberg, B.      44 269
Elementary events      1
Elementary events, space of      1
Enger, J.      36
Erdoes Ч Renyi law      235
Erdoes, P.      77 137 199 226 235 267Ч9 275 277 283
Erickson, K.B.      231 269
Esseen's inequality      149
Esseen's theorem      142
Esseen, C.-G.      36 47 77 81Ч82 87 142 147 149Ч150 155 176Ч177 181 183Ч185 187 191 265 269 270 272Ч274 277 281 284Ч285
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 110Ч111 120Ч121 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.      77Ч78 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 110Ч111 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 Ч Renyi inequality      54
Hajek, J.      54 77 268 271
Hall, P.      40 87 139 174 184Ч185 190 194Ч198 227 238 265 268 271Ч272
Hardy, G.H.      272
Hartman Ч 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 184Ч185 188Ч190 193 196 226Ч227 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 107Ч108 185Ч186 188 193 195Ч196 273
Independent events      4
Independent events, random variables      4Ч6
Infinite smallness      88
Infinitely divisible distributions      28Ч36 47Ч49 91 98Ч103 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.      137Ч138 140 184 229 231 265 273
Kawata concentration function      44Ч45
Kawata, T.      38Ч39 44Ч45 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 111Ч112 134 255 274
Kingman, J.F.C.      36 274
Kirsha, K.      42 266
Klaassen, C.A.J.      37 274
Klass, M.J.      255Ч256 274
Kochen, S.B.      226 274
Kolmogorov Ч 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 68Ч69 73 77 101 105 107 134 185 205 226 239 255 263 265 267 271 274 280Ч281 284
Kolodyazhny, S.F.      185 274
Komlos Ч Major Ч Tusnady approximation      236Ч237
Komlos, J.      227 235-237 266 268 274 284
Koopmans, L.H.      270
Kroneeker's lemma      209 212Ч213 249
Kruglov, V.M.      48 107 111 229 274Ч275
Kunisawa concentration function      45Ч46
Kunisawa, K.      45Ч47 275
Lacey, M.I.      238 275
Lai, T.L.      138 232 267Ч268
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      127Ч128 131
Law or the iterated logarithm      239 248
Lebesgue decomposition theorem      3
LeCam, L.      107 275
Leslie, J.R.      184 196 272 275
Levy Ч Khintchine formula      30 112
Levy Ч Khintchine formula, spectral function      34
Levy Ч 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 34Ч36 40 43Ч45 47Ч49 65 77 87 99 103 105 107 111Ч112 120 126 134 176 219 266 269 274 275 279
Lifshits, B.A.      196 275
Lin, Z.Y.      235 275
Lindeberg condition      124Ч126
Lindeberg ratio      124 154 247Ч248
Lindeberg Ч Feller theorem      123
Lindeberg, J.W.      123Ч124 126 135 273 278 282
Linnik, Yu.V.      36 105 108 185Ч186 273 275
Littlewood, J.E.      272
Loeve, M.      1 36 107Ч108 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 265Ч266 270 275 278 285
Lynch, J.      235 275
Maejima, M.      42 189 275
Major, P.      236Ч238 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 228Ч229 232 234 238 255Ч257 262Ч263 276Ч277
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 77Ч78 185 191 226Ч228 271 277Ч278 284
Nakata, T.      185 190 193 198 272
Nikitenko, T.V.      260 278
O'Brien, G.L.      226
Ohkubo, H.      48Ч49 278
Osipov's theorem      158 167 173
Osipov, L.V.      158 167 173 184Ч185 194 275 278
Ostrovskii, I.V.      36 275
Paditz, L.      185 278
Pakshirajan, R.P.      47 267
Paulauskas, V.I.      184Ч186 191 278
Peter, E.      227 266
Petrov, V.V.      36Ч37 77 80 81 84 101 111 137 140Ч141 173Ч174 184Ч187 224 226 229Ч230 233Ч234 238 255 261 263Ч264 269 275 277Ч280
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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