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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

Independent, mean and variance of normal sample      119 122 211
Independent, normal r.v.s      101
Independent, p.g.f.      154
Independent, pairwise      13 14 155
Independent, set      88
Independent, triplewise      155
Indicator r.v.      29 56
Indicator r.v., linear combinations of      43 48
Indicator r.v., matching      56
Indicator r.v., moments      52
Indicator r.v., structure fn      58
Inequality, $C_{p}$       319
Inequality, Bernstein      32
Inequality, Bonferroni      25
Inequality, Boole      22
Inequality, Cauchy - Schwarz      65 102
Inequality, Chebyshov      319
Inequality, Doob $L_{2}$       539
Inequality, Doob - Kolmogorov      338 342 497
Inequality, downcrossings      486
Inequality, Dubins      485
Inequality, FKG      85
Inequality, H $\acute{a}$ jek - R $\acute{e}$ nyi - Chow      508
Inequality, H $\ddot{o}$ lder      143 319
Inequality, Hoeffding      476
Inequality, Jensen      181 349
Inequality, Kolmogorov      342 358 498 508
Inequality, Kounias      25
Inequality, Lyapunov      143
Inequality, Markov      311 318
Inequality, maximal      489 490 496
Inequality, Minkowski      143 319
Inequality, triangle      306 343
Inequality, upcrossings      482 486
Infinitely divisible distn      207 208
Inspection paradox      421 437
Instantaneous, mean and variance      519
Instantaneous, state      266
Insurance      470 510
Integral, abstract      178
Integral, It $\hat{o}$       538 542
Integral, Lebesgue - Stieltjes      180
Integral, Monte Carlo      42 141
Integral, Riemann      538
Integral, Stochastic      388 411 538
Integral, Stratonovich      538
Integral, surface i.      555
Integral, transforms      566
Intensity, of birth pr.      250
Intensity, of Poisson pr.      282
Intensity, traffic i.      369 441
Interarrival time      248 368 374 412
Invariant, $\sigma$ -field      399 405
Invariant, event      398
Inverse distn      35
Inverse square distn      47 54
Inverse transform technique      122
Inversion theorem, c.f.      189
Inversion Theorem, Fourier      189 383
Inversion theorem, Lagrange      166
Invisible customers      463
Irreducible chain and set      224 232
Irreducible chain and set of Markov pr.      260 298
Ising model      292
Isometric isomorphism      391 540
It $\hat{o}$ , formula      538 545
It $\hat{o}$ , integral      538 542
It $\hat{o}$ , process      542 544
It $\hat{o}$ , product rule      546
It $\hat{o}$ , simple formula      545
Iterated logarithm      332
Jackson network      463
Jacobian      108
Jaguar      17 42 74 86
jargon      3
Jensen's inequality      181 349
Joint, c.f.      183 209
Joint, density      40 98
Joint, distn      39 63 98
Joint, mass fn      39 63
Joint, moments      209
Joint, transformed r.v.s      108 112
Jordan form      241
Jump chain      261
Jump chain imbedded      265 274 445
Key renewal theorem      418
Keynes, J. M.      75
Killing      531
Kirchhoff's laws      559
Knapsack problem      481
Kolmogorov - Doob inequality      338 342 497
Kolmogorov - Fisher eqn      522
Kolmogorov, consistency conditions      371 405
Kolmogorov, criterion      239
Kolmogorov, eqns      267
Kolmogorov, inequality      342 358 498 508
Kolmogorov, zero-one law      322 400
Korolyuk - Khinchin theorem      365
Kounias's inequality      25
Krickeberg decomposition      510
Kronecker, delta fn      221 564
Kronecker, lemma      342
kurtosis      145
Labouchere system      510
Lack of anticipation      265
Lack-of-memory property, of exponential distn      140
Lack-of-memory property, of geometric distn      84
Lack-of-memory property, of holding time      259
ladders      458 459 461
Lagrange's formula      166
Lancaster's theorem      144
Langevin eqn      516
Laplace - de Moivre thm      96 195
Laplace - Stieltjes transform      416 567
Laplace, convolution      567
Laplace, L. eqn      554 556 557
Laplace, method of steepest descent      192
Laplace, transform      181 442 566
Large deviations      32 202 477
Last exits      223
Lattice, cubic      514 560
Lattice, distn      185
Lattice, square      279 560
Law, arc sine      80 81 83 86 170 529 563
Law, convergence in      193 309
Law, De Morgan      4
Law, of anomalous numbers      66
Law, of iterated logarithm      332
Law, of large numbers      193 326
Law, of unconscious statistician      50 64 83 93 99
Law, strong      326 329
Law, weak      193 326
Law, zero-one      321 322 324 400 484
Lazy, landlord      424
Lazy, pupil      39
Leads in tied down r.w.      169
Lebesgue - Stieltjes integral      180
Lebesgue measure      281 300 315
Left-continuous r.w.      165
Legendre polynomial      558
Level sets of Wiener pr.      562
Levy, characterization      502
Levy, dichotomy      267
Levy, martingale      347 484
Levy, metric      44 308 318
Life, current      366 421 423
Life, excess      255 366 421 423
Life, total      366 421
Light bulbs      365 412 426
Likelihood ratio      358 504

Limit, binomial      84
Limit, binomial-Poisson      61 130 210
Limit, branching      174
Limit, central limit theorem      194
Limit, diffusion      515
Limit, ergodic      393 394
Limit, events      7 23
Limit, extreme-value      145
Limit, gamma      192
Limit, geometric-exponential      95 210
Limit, immigration-death      270
Limit, l. distns      35 308
Limit, lim inf      23 565
Limit, lim sup      23 565
Limit, local central l. thm      195
Limit, Markov chain      232
Limit, martingale      481
Limit, Poisson      85 87 129
Limit, r.v.      43 179
Limit, r.w.      483
Limit, renewal      160 412
Lindley's eqn      455
Linear fn of normal r.v.      117 118
Lipschitz continuity      507
Little's theorem      435
Local balance      239
Local central limit thm      195
Locked counter      423 437
Log-convex      47
Log-likelihood      358
Log-normal distn      97 211
Logarithm iterated      332
Logarithmic distn      47 161
Long run average waiting time      435
Los Alamos      43
Lottery      24
Lucky customer      460
Lyapunov's inequality      143
M $\acaute{e}$ nages      23
machine      470
Magnets      60
Malthusian parameter      430
Mapping theorem      284
Marginal, bivariate normal      100
Marginal, density      99
Marginal, discontinuous      102
Marginal, distn      39 99
Marginal, mass fn      63
Marginal, of multinomial      66
Marginal, order statistics      142
Marilyn vos Savant      11
Markov - Kakutani theorem      242
Markov chain      214
Markov chain in continuous time      256
Markov chain in continuous time, backward eqns      259 267
Markov chain in continuous time, Chapman-Kolmogorov eqns      256
Markov chain in continuous time, classification      260 263
Markov chain in continuous time, ergodic thm      261 358
Markov chain in continuous time, explosion      262
Markov chain in continuous time, first passage      433
Markov chain in continuous time, forward eqns      259 267
Markov chain in continuous time, generator      258
Markov chain in continuous time, holding time      259 261 433
Markov chain in continuous time, homogeneous      256
Markov chain in continuous time, irreducible      260 298
Markov chain in continuous time, jump chain      261 265 274
Markov chain in continuous time, Kolmogorov eqns      267
Markov chain in continuous time, martingale      501 543
Markov chain in continuous time, mean recurrence time      265 433
Markov chain in continuous time, minimal      262
Markov chain in continuous time, non-homogeneous      274 300
Markov chain in continuous time, renewal pr.      366 416
Markov chain in continuous time, reversible      299 469
Markov chain in continuous time, sampled      264
Markov chain in continuous time, skeleton      261
Markov chain in continuous time, stationary distn      260
Markov chain in continuous time, transition matrix      256
Markov chain in continuous time, two-state      260 264 267 384
Markov chain in continuous time, visits      265 433
Markov chain in discrete time      214
Markov chain in discrete time, Chapman-Kolmogorov eqn      215
Markov chain in discrete time, classification of      220 222
Markov chain in discrete time, coupled      233
Markov chain in discrete time, decomposition of      224
Markov chain in discrete time, ergodic thm      235 358 402 429
Markov chain in discrete time, finite      225
Markov chain in discrete time, first passage of      220 226
Markov chain in discrete time, generating fns      221
Markov chain in discrete time, homogeneous      214
Markov chain in discrete time, imbedded      219 265 274 299 446 452
Markov chain in discrete time, limit thm for      232
Markov chain in discrete time, M.'s other chain      218
Markov chain in discrete time, martingale      335 341 473 480 486 492
Markov chain in discrete time, mean first passage      226
Markov chain in discrete time, mean recurrence time      222
Markov chain in discrete time, renewal      297 421
Markov chain in discrete time, reversed M.c.      237
Markov chain in discrete time, reversible      238
Markov chain in discrete time, stationary distn for      227
Markov chain in discrete time, transition matrix      214
Markov chain in discrete time, two-state      239 298 364
Markov chain in discrete time, visits by      223 226 297 303
Markov chain Monte Carlo      292
Markov condition      214
Markov inequality      311 318
Markov process, Gaussian      406 408
Markov process, stationary      227 260 407 408
Markov property      214 256
Markov property of branching pr.      216
Markov property of r.w.      73 216
Markov property, strong      219 253 526
Markov property, weak      253 525
Markov renewal pr.      366 416
Markov time      487; see Stopping time
Markovian queue      280 369 442 468 470
Marriage problem      144
Martingale      333 471 474 543
Martingale, backward      499
Martingale, birth-death pr.      509
Martingale, branching pr.      334 475 508 509
Martingale, closed      484
Martingale, continuous parameter      501 502 512 528 534 543 546 551
Martingale, convergence of      338 481 498 502
Martingale, de Moivre m.      472 483 486 492
Martingale, diffusion pr.      542
Martingale, Doob's m.      347 484
Martingale, epidemic      505
Martingale, excursions of      534
Martingale, exponential m.      525 528
Martingale, gambling      333 338 471 475 496 503 511
Martingale, genetic model      341
Martingale, It $\hat{o}$ integral      543
Martingale, L $\acute{e}$ vy m.      347 484
Martingale, m. differences      476
Martingale, m. representation      543
Martingale, m. transform      503
Martingale, Markov chain      335 341 473 480 486 492
Martingale, optional stopping      488 491 503
Martingale, partial sum of      335
Martingale, reversed m.      499
Martingale, s.r.w.      471 472 475 483 486 490 492 494 496
Martingale, stochastic integral      543
Martingale, submartingale      474
Martingale, supermartingale      474 475 486
Martingale, with respect to filtration      474
Mass function      46
Mass function, conditional      67
Mass function, joint      39 63
Mass function, marginal      63
Mass, centre of      50

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