Grimmett G., Stirzaker D. — Probability and Random Processes :: Электронная библиотека попечительского совета мехмата МГУ

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Grimmett G., Stirzaker D. — Probability and Random Processes

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Название: Probability and Random Processes

Авторы: Grimmett G., Stirzaker D.

Аннотация:

The volume will be useful to all those teachers of probability and random processes who set work assignments and examinations.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd Edition

Год издания: 2001

Количество страниц: 608

Добавлена в каталог: 05.04.2008

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

Предметный указатель

$C_{p}$ inequality      319
$L_{2}$ , inequality      539
$L_{2}$ , norm      343
$L_{p}$ norm      343
th mean convergence      308
$\mathcal{F}$ -measurable      27 92
$\sigma$ -field      3 14 21
$\sigma$ -field, conditioning on      346
$\sigma$ -field, decreasing sequence of      499
$\sigma$ -field, increasing sequence of      347 473
$\sigma$ -field, invariant      399
$\sigma$ -field, tail      322
$\sigma$ -field, trivial      323
Abel's theorem      151 221
Absolute convergence      50
Absolutely continuous      33
Absorbing barrier, in diffusion pr.      530 531 561 562
Absorbing barrier, in r.w.      18 72 74
Absorbing state      224 266
Abstract integral      178
Acceptance probability      293
Adapted process      539 543
Adapted sequence      473 501
Additive probability measure      5
Affine transformation      136
Age of renewal process      366 421
Age-dependent branching process      176 273 430 438 508
Age-dependent branching process honest      273
Age-dependent branching process Malthusian parameter      430
Age-dependent branching process mean      177
Airlines      25 44
Alarm Clock      299
Algorithm      293 294 296
Aliasing method      126
Almost sure convergence      180 308
Almost surely (a.s.)      7
Alternating renewal pr.      425 436 438
Alternative measure      549
American call option      554
Ancestors in common      175
Ancillary distn      203
Anomalous numbers      66
Anscombe's theorem      358
Antithetic variable      126
Ants      302
Aperiodic set      224
Aperiodic state      222
Arbitrage      55 242 548 551
Arbuthnot, J.      86 573
Arc sine distn, sampling from      127
Arc sine laws for r.w., maxima      86 91
Arc sine laws for r.w., sojourns      81 170
Arc sine laws for r.w., visits      80 83
Arc sine laws for Wiener pr.      529 563
Arithmetic r.v.      192 417 422 428
arrows      135
atom      34 50
atomic      33
Autocorrelation function      380
Autocorrelation function, spectral thm for      381
Autocovariance function      361 380
Autocovariance function, non-negative definite      380
Autoregressive scheme      364 378 385
Autoregressive sequence      374
Autoregressive sequence, spectral density of      386
Auxiliary pr.      465
Average      50 93
Average moving      363 373 393
Backward equations, birth pr.      251
Backward equations, birth-death pr.      272
Backward equations, diffusion pr.      519
Backward equations, Markov pr.      259 267
Backward equations, Wiener pr.      517
Backward martingale      499
Balance equations      238 293
Ballot Theorem      77 500
Balls in boxes      130
Bandrika      25 92
Bankruptcy      see Gambler's ruin
Barker's algorithm      296
Barriers, absorbing/reflecting in diffusion      530 531 533
Barriers, absorbing/retaining in r.w.      74
Barriers, hitting by Wiener pr.      529
Bartlett, equation      524
Bartlett, thm      374
Batch service      468
Baulking      369 468 470
Bayes's formula      22
Bayesian inference      292
Bears      291 439
Benford's distn      66
Berkeley      20
Berkson's fallacy      88
Bernoulli c.f.      186
Bernoulli distn      29 60
Bernoulli moments      52 60
Bernoulli p.g.f.      151
Bernoulli sampling from      123
Bernoulli sum of      47 60 85 129 153
Bernoulli's theorem      31
Bernoulli, Daniel      55 59
Bernoulli, James      31
Bernoulli, model      302
Bernoulli, Nicholas      55
Bernoulli, pr.      218
Bernoulli, renewal pr.      374
Bernstein's inequality      32 203 477
Bertrand's paradox      133 141
Bessel, function      442 468 470
Bessel, process      512 525
Best predictor      343 346 378
Beta, -binomial      107
Beta, distn      97
Beta, sampling from      126
Betting scheme      242
Bin packing      477
Binary expansion      377 402 410
Binary fission      177
Binary tree      210
Binary tree r.w. on      236
Binomial distn      47 60
Binomial distn c.f.      186
Binomial distn distn      47 60
Binomial distn limits      61 130 195 210
Binomial distn moments      52 60
Binomial distn p.g.f.      153
Binomial distn sampling from      123
Binomial distn sum of      84 153
Birth process      250 255
Birth process dishonest      252 267
Birth process forward and backward eqns      251
Birth process generator      258
Birth process honest      252
Birth process immigration      255
Birth process minimal      251
Birth process non-homogeneous      300
Birth process uniform      268 (see also simple birth)
Birth-death process      269
Birth-death process backward eqn      272
Birth-death process coupled      303
Birth-death process extinction      272 275 300 509
Birth-death process forward eqn      271
Birth-death process generator      269
Birth-death process immigration      276
Birth-death process martingale      509
Birth-death process non-homogeneous      274
Birth-death process queue      281 442
Birth-death process stationary distn      269
Birth-death process uniform      269 (see also Simple birth-death)
Birthdays      24 42

Bivariate, branching pr.      275
Bivariate, negative binomial distn      208
Bivariate, normal distn      100 106 111 112 114 118 141 349
Bivariate, p.g.f.      154
Black - Scholes, eqn      552
Black - Scholes, formula      551
Black - Scholes, model      547 563
Black - Scholes, value      554
Boat race      1
Bochner's theorem      182 381
BOND      547
Bonferroni's inequality      25
Books      45
Boole's inequalities      22
Borel - Cantelli lemmas      320
Borel, field      91 180 315 398
Borel, field measurable      92
Borel, field normal number thm      410
Borel, field paradox      106
Borel, field set      91 281 372
Bounded convergence      180 229
Bow tie      237
Box - Muller normals      126
Boxes      281
Boys      9 86
Branching process      171
Branching process age-dependent      176 273 430 438 508
Branching process, bivariate      275
Branching process, busy period      450
Branching process, conditioned      177 208 243 246
Branching process, convergence      509
Branching process, critical      245
Branching process, diffusion      521
Branching process, diffusion approximation      520
Branching process, dishonest      273
Branching process, explosion      273
Branching process, extinction      173
Branching process, family tree      171
Branching process, geometric      172
Branching process, honest      273
Branching process, imbedded      177 272 450
Branching process, immigration      175 338 508
Branching process, Malthusian parameter      430
Branching process, Markov      216
Branching process, martingale      334 475 508 509
Branching process, moments      172 207
Branching process, p.g.f.      171
Branching process, r.w.      278
Branching process, stationary distn      245
Branching process, sub/supercritical      245
Branching process, total population      207
Branching process, transition matrix      216
Branching process, variance      172 207
Bridge      24
Brownian bridge      411 535
Brownian bridge, autocovariance      536
Brownian bridge, zeros      536
Brownian motion      370 514
Brownian motion geometric      525 537 546
Brownian motion tied down      411
Buffon's cross      103
Buffon's needle      100 103 134 143 144 305
Buffon's noodle      143
Buffon's weldings      128
Busy period      281
Busy period branching pr.      450
Busy period in M/G/l      447
C $\grave{a}$ dl $\grave{a}$ g      373
Cake      87
Call option, American      554
Call option, European      548 552 554
Campbell - Hardy theorem      290 291
Cancer      280 298
Canonical form      241
Cantelli      see Borel- - Cantelli
Capture-recapture      62
Car wash      436
Cardinality      6 564
cards      16 24 25 235
Carroll, Lewis      12 135
Casanova      333
casino      71 75 333 338 472 488 511
Cauchy - Schwarz inequality      65 102
Cauchy c.f.      186
Cauchy complete      540
Cauchy convergence      309 323 565
Cauchy convergence in m.s.      355
Cauchy distn      97 140 146 385
Cauchy maximum      356
Cauchy moments      97
Cauchy sampling from      126
Cauchy sum of      115 206 209 328
cells      275
Central limit thm      194 200 417 515
Central moments      51
Certain event      2
Ces $\grave{a}$ ro average      292
Chain      see Markov
Chain rule      538
Chamber      236
Change, exponential      203
Change, of measure      549
Change, of variables      108 112
Chapman - Kolmogorov eqns      215 256
Characteristic function      182
Characteristic function, autocorrelation fn      381
Characteristic function, Bernoulli distn      186
Characteristic function, binomial distn      186
Characteristic function, Cauchy distn      186
Characteristic function, central limit thm      194
Characteristic function, chi-squared distn      188
Characteristic function, continuity thm      190
Characteristic function, exponential distn      186
Characteristic function, extreme-value distn      209
Characteristic function, first passage distn      200
Characteristic function, gamma distn      188
Characteristic function, infinitely divisible      208
Characteristic function, inversion      189
Characteristic function, joint      183 209
Characteristic function, law of large numbers      328
Characteristic function, m.g.f.      184
Characteristic function, moments      183
Characteristic function, multinormal distn      187
Characteristic function, normal      187
Characteristic function, positive definite      182
Characteristic function, sum of independent r.v.      183
Chebyshov's inequality      319
Cherries      23
Chess      242
Chi-squared ( $\chi^{2}$ ) distn      97 119
Chi-squared ( $\chi^{2}$ ) distn c.f.      188
Chi-squared ( $\chi^{2}$ ) distn non-central      185
Chi-squared ( $\chi^{2}$ ) distn sum of      122 141
Chicks      68 154
Chimeras      87
Cholesky decomposition      147
Chromatic number      481
circle      133 138 141 146 556
Classification, Markov chain      224
Classification, Markov pr.      260
Classification, of states      220 222
Closed, linear space      344
Closed, martingale      484
Closed, migration pr.      464
Closed, set      224
Coins, double      12
Coins, fair      5 6 14 80 81
Coins, first head      3 8 43 487
Coins, gambler's      26
Coins, patterns      162 206 511

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