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Grimmett G., Stirzaker D. — Probability and Random Processes |
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Предметный указатель |
inequality 319
, inequality 539
, norm 343
norm 343
th mean convergence 308
-measurable 27 92
-field 3 14 21
-field, conditioning on 346
-field, decreasing sequence of 499
-field, increasing sequence of 347 473
-field, invariant 399
-field, tail 322
-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
Cdlg 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
Cesro 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 () distn 97 119
Chi-squared () distn c.f. 188
Chi-squared () distn non-central 185
Chi-squared () 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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