Feller W. — Introduction to probability theory and its applications (volume 1) :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Feller W. — Introduction to probability theory and its applications (volume 1)

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Introduction to probability theory and its applications (volume 1)

Автор: Feller W.

Аннотация:

Major changes in this edition include the substitution of probabilistic arguments for combinatorial artifices, and the addition of new sections on branching processes, Markov chains, and the De Moivre-Laplace theorem.

Язык:

Рубрика: Математика/Вероятность/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1967

Количество страниц: 509

Добавлена в каталог: 29.05.2005

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

Предметный указатель

Morse code      54
moving averages      422 426
Multinomial coefficients      37
Multinomial distribution      167 215 239
Multinomial distribution generating function      279
Multinomial distribution maximal term      171 194
Multinomial distribution randomized      216 301
Multiple Bernoulli trials      168 171 238
Multiple classification      27
Multiple coin games      316 338
Multiple Poisson distribution      172
Multiplets      27
Murphy, G.M. and Margenau, H.      41
Mutations      295
M’Kendrick, A.G.      450
Negation      15
Negative binomial distribution      164ff. 238
Negative binomial distribution as limit of Bose — Einstein statistics      61
Negative binomial distribution as limit of Bose — Einstein statistics and of Polya distr.      143
Negative binomial distribution expectation      224
Negative binomial distribution generating function      268
Negative binomial distribution in birth and death processes      450
Negative binomial distribution infinite divisibility      289
Negative binomial distribution, bivariate      285
Negative binomial distribution, Poisson limit of      166 281
Nelson, E.      96
Newman, D.J.      210 367
Newton, I.      55
Newton’s binomial formula      51
Neyman, J.      163 285
Non-Markovian processes      293 421 426
Non-Markovian processes satisfying Chapman — Kolmogorov equation      423 471
Normal approximation for binomial distribution      76 179ff.
Normal approximation for binomial distribution large deviations      192 195
Normal approximation for changes of sign      86
Normal approximation for combinatorial runs      194
Normal approximation for first passages      90
Normal approximation for hypergeometric distribution      194
Normal approximation for permutations      256
Normal approximation for Poisson distribution      190 194 245
Normal approximation for recurrent events      321
Normal approximation for returns to origin      90
Normal approximation for success runs      324 (cf. “Central limit theorem”)
Normal density and distribution      174
Normal density and distribution tail estimates      179 193
Normalized random variables      229
Nuclear chain reaction      294
Null state      388
Number theoretical interpretations      208
Occupancy numbers      38
Occupancy problems      38ff. 58ff. 101ff. 241
Occupancy problems empirical interpretations      9
Occupancy problems multiply occupied cells      112
Occupancy problems negative binomial limit      61
Occupancy problems Poisson limit      59 105
Occupancy problems treatment by Markov chains      379 435
Occupancy problems treatment by Markov chains and by randomization      301
Occupancy problems waiting times      47 225
Occupancy problems waiting times, elementary problems      27 32 35 55 141 237 “Bose “Collector’s
Optional stopping      186 241
Orderings      29 36 “Runs combinatorial”)
Ore, O.      56
Orey, S.      413
Pairs      26
Palm, C.      460 462
Panse, V.G. and Sukhatme, P.V.      150
Parapsychology      56 407
Parapsychology Guessing      107
Parking lots      55 479
Parking tickets      55
Partial derivatives      39
Partial fraction expansions      275ff. 285
Partial fraction expansions explicit calculations for reflecting barrier      436ff.
Partial fraction expansions for finite Markov chains      428ff.
Partial fraction expansions for ruin problem      349ff.
Partial fraction expansions for ruin problem and for success runs      322ff.
Partial fraction expansions numerical calculations      278 325 334
Particular solutions, method of      344 347 365
Partitioning of polygons      283
Partitioning of stochastic matrices      386
Partitions, combinatorial      34ff.
Pascal, B.      56
Pascal’s distribution      166
Pathria, R.K.      32
Paths in random walks      68
Pearson, K.      173 256
Pedestrians as non-Markovian process      422
Pedestrians crossing the street      170
Pepys, S.      55
Periodic Markov chains (states)      387 404ff.
Periodic recurrent events      310
permutations      29 406
Permutations represented by independent trials      132 256ff.
Persistent recurrent event      310
Persistent recurrent event limit theorem      335
Persistent state      388
Petersburg Paradox      251
Petri plate      163
Phase space      13
Photographic emulsions      11 59
Poisson approximation or limit for Bernoulli trials with variable probabilities      282
Poisson approximation or limit for binomial distr.      153ff 172 190
Poisson approximation or limit for density fluctuations      425
Poisson approximation or limit for hyper-geometric distr.      172
Poisson approximation or limit for long success runs      341
Poisson approximation or limit for matching      108
Poisson approximation or limit for negative binomial      172 281
Poisson approximation or limit for normal distr.      190 245
Poisson approximation or limit for occupancy problems      105 153
Poisson approximation or limit for stochastic processes      461 462 480 481
Poisson distribution (the ordinary)      156ff.
Poisson distribution convolutions      173 266
Poisson distribution empirical observations      159ff.
Poisson distribution generating function      268
Poisson distribution integral representation      173
Poisson distribution moments      224 228
Poisson distribution normal approximation      190 194 245
Poisson distributions bivariate      172 279
Poisson distributions compound      288ff. 474
Poisson distributions generalized      474
Poisson distributions multiple      172
Poisson distributions spatial      159
Poisson distributions spatial combined with binomial distr.      171 287 301
Poisson process      292 446ff.
Poisson process backward and forward equs.      469—470
Poisson process generalized      474
Poisson traffic      459
Poisson trials (= Bernoulli trials with variable probabilities)      218 230 282
Poisson, S.D.      153
Poker definition      8
Poker tabulation      487
Poker, Elementary problems      35 58 169
Pollard, H.      312
Polya process      480
Polya urn model      120 142 240 262 480
Polya urn model as non-Markovian process      421
Polya’s distribution      142 143 166 172
Polygons, partitions of      283
Polymers      11 240
Population      34ff.
Population growth      334—335 450 456
Population in renewal theory      334—335 340
Population, stratified      117
Positive state      389
power supply problems      149 467
Product measure      131
Product spaces      128ff.
Progeny (in branching processes)      298ff.
Prospective equations      cf. “Forward equations”
Quality control      42 (cf. “Inspection sampling”)

Queue discipline      479
Queuing and queues      306 315 460ff. 479
Queuing and queues a Markov chain in queuing theory      425
Queuing and queues as branching process      295 299—301
Queuing and queues general limit theorem      320
Radiation      cf. “Cosmic rays” “Irradiation”
Radioactive disintegrations      157 159 328
Radioactive disintegrations, differential equations for      449
Raff, M.S.      240
Raisins, distribution of      156 169
Random chains      240
Random choice      30
Random digits (= random sampling numbers)      10 31
Random digits normal approximation      189
Random digits Poisson approximation      155
Random digits, Elementary problems      55 169
Random digits, references to      21 61
Random mating      134
Random placement of balls into cells      cf. “Occupancy problems”
Random sampling      cf. “Sampling”
Random sums      286ff.
Random variables      212ff.
Random variables, defective      273 309
Random variables, integral valued      264ff.
Random variables, normalized      229 (cf. “Independent Random variables”)
Random walks      67ff. 342ff.
Random walks cyclical      377 434
Random walks invariant measure      408
Random walks Markov chain treatment      373 376—377 425 436ff.
Random walks renewal method      370
Random walks reversibility      415
Random walks with variable probabilities      402 (cf. “Absorbing barrier” “Arc “Changes “Diffusion” “Duration “First “Leads” “Maxima” “Reflecting “Returns “Ruin
Random walks, dual      91
Random walks, generalized      363ff. 368
Randomization method in occupancy problems      301
Randomization method in sampling      216 (cf. “Random sums”)
Randomness in sequences      204
Randomness in sequences, tests for      42 61
RANGE      213
Rank order test      69 94
Ratio limit theorem      407 413
Realization of events, simultaneous      16 99 106 109 142
Recapture in trapping experiments      45
Recessive genes      133
Recessive genes sex-linked      139
Recurrence times      388
Recurrence times in Markov chains      388 (cf. “Renewal theorem”)
Recurrent events      310ff.
Recurrent events reversibility      415 (cf. “Renewal theorem”)
Recurrent events, delayed      316ff.
Recurrent events, Markov chain treatment of      381—382 398 403
Recurrent events, number of occurrences of a      320ff.
Reduced number of successes      186
Reflecting barriers      343 367ff.
Reflecting barriers invariant distribution      397 424
Reflecting barriers two dimensions      425
Reflecting barriers, Markov chain for      376 436ff.
Reflection principle      72 369
Reflection principle, Repeated reflections      96 369ff.
Rencontre (= matches)      100 107
Renewal argument      331
Renewal method for random walks      370
Renewal of aggregates and populations      311 334—335 340 381
Renewal Theorem      329
Renewal theorem, estimates to      340
Renewal theorem, estimates to, for Markov chains      443
Repairs of machines      462ff.
Repeated averaging      333 425
replacement      cf. “Renewal” “Sampling”
Residual waiting time      332 381
Retrospective equations      cf. “Backward equations”
Return process      477
Returns to origin first return      76—78 273 313
Returns to origin in higher dimensions      360
Returns to origin nth return      90 274
Returns to origin through negative values      314 339
Returns to origin visits prior to first      376 (cf. “Changes of sign” “First
Returns to origin, number of      96
Reuter, G.E. and Ledermann, W.      455
Reversed Markov chains      414ff.
Riordan, J.      73 299 306
Robbins, H.E.      53
Romig, H.C.      148
Ruin problem      342ff.
Ruin problem in generalized random walk      363ff.
Ruin problem renewal method      370
Ruin problem with ties permitted      367
Rumors      56
Runs, combinatorial      42 62
Runs, combinatorial moments      240
Runs, combinatorial normal approximation      194 (cf. “Success runs”)
Rutherford — Chadwick — Ellis      160
Rutherford, E.      170
Sacks, L. and Li, C.C.      144
Safety campaign      121
Sample point      9
Sample space      4 9 13ff.
Sample space discrete      17ff.
Sample space for repeated trials and experiments      128ff.
Sample space in terms of random variables      217
Sampling      28ff. 59 132 232
Sampling required sample size      189 245
Sampling waiting times      224 239
Sampling waiting times, Elementary problems      10 12 56 117 194 “Inspection
Sampling, randomized      216
Sampling, sequential      344 363
Sampling, stratified      240
Savage, L.J.      4 346
Schell, E.D.      55
Schensted, I.V.      379
Schroedinger, E.      294
Schwarz’ inequality      242
Seeds Poisson distribution      159
Seeds survival      295
Segregation, subnuclear      379
Selection (genetic)      139 143 295
Selection principle      336
Self-renewing aggregates      311 334 340
Senator problem      35 44
Sequential sampling      344 363
Sequential tests      171
Sera, testing of      150
Servers      cf. “Queuing” “Trunking
Service times      457ff.
Service times as branching process      288
Servicing factor      463
Servicing problems      460 479
Seven-way lamps      27
Sex distribution within families      11 117 118 126 169 288
Sex-linked characters      136
Shewhart, W.A.      42
Shoe problems      57 111
Shuffling      406
Shuffling, composite      422
Simulation of a perfect coin      238
Small numbers, law of      159
Smirnov, N.      70 71
Smith, B. and Kendall, M.G.      154
Sobel, M. and Groll, P.A.      239
Sojourn times      82 453
Sparre-Andersen, E.      82
Spent waiting time      382
Spores      226 379
Spurious contagion      121
Stable distribution of order one half      90
Stakes (effect of changing)      346
Standard deviation      228
Stars (Poisson distribution)      159 170
States in a Markov chain      374 446
States in a Markov chain absorbing      384

1 2 3 4

О проекте