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Feller W. Ч Introduction to probability theory and its applications (Volume II)
Feller W. Ч Introduction to probability theory and its applications (Volume II)

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Ќазвание: Introduction to probability theory and its applications (Volume II)

јвтор: Feller W.

јннотаци€:

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: en

–убрика: ћатематика/

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

ed2k: ed2k stats

»здание: 2nd edition

√од издани€: 1971

 оличество страниц: 669

ƒобавлена в каталог: 14.09.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel summability      627 628 648
Abelian theorems      418 445
AbelТs integral equation      33
Absolute continuity      139 140
Absolute probabilities      207Ч209
Absolutely fair      210
Absolutely monotone functions      223Ч224 439 441
Absorbing barriers      340Ч342 464 477Ч479
Absorption (physical)      25 31 323
Accidents      57 181
Additive set functions      107
Additive set functions, countably = sigma      108 119 129Ч130
Age      see УDurationФ
Algebra of sets      112Ч113 116
Algebra of sets, generation of      163
Ambarzumian, V.A.      206 325
Anomalous numbers      63
Arc sine distributions      50
Arc sine distributions and limit theorems      470Ч473
Arc sine distributions in random walks      417Ч423
Arithmetic distributions      138 407Ч408
Arrays, null      177Ч178 585
arrays, triangular      177Ч178 216 308Ч312 583Ч588 596
Arzela Ч Ascoli theorem      270
Ascending ladder variables, strict      391
Ascending ladder variables, weak      392Ч393
Associated random walks      406
Astronomy, applications to      33 172 173Ч174 206 215 325Ч326
Asymptotic behavior      521 572
Asymptotic estimates      375Ч377 410Ч411
Asymptotic properties of regularly varying functions      279Ч284
Asymptotically dense      147
Asymptotically negligible      178
Asymptotically unbiased estimators      220
Atomic measures      137Ч138
Atoms (of measures)      137
Atoms (of measures), under convolutions      147 149 166
Attraction      see УDomain of attractionФ
Auto-regressive process      89 96
Bachelier process      see УBrownian motionФ
Backward equations      357
Backward equations for diffusion      334 336Ч337 344
Backward equations for jump processes      327Ч328 484Ч487
Backward equations for semi-groups      352 356Ч357
Backward equations for semi-Markov processes      497
Backward equations of Kolmogorov      327Ч328
Backward equations, minimal solution of      322 329Ч331 486
Bad luck      15Ч17
Baire functions      104Ч106 109 114 130 305 351
Banach space      257 350 487
Barriers      see УAbsorbing barriersФ УBoundary УReflecting
Barucha-Reid, A.T.      656
Baxter, G.      404 424 571 605
Bayes, T.      56
Benes, V.E.      379 656
Benford, F.      63
Bergstroem, H.      581
Bernouilli trials      1 141Ч142
Bernstein polynomials      222Ч223
Bernstein polynomials in $R^{2}$      245
Bernstein, S.      79 439
Berry Ч Esseen theorems      538 542Ч546 551
Berry, A.C.      531 536 542
Bessel density      502
Bessel functions      58Ч61 523
Bessel functions and infinite divisibility      177 451 566
Bessel functions and Laplace transforms      437 438 479Ч482
Bessel functions and related distributions      58Ч61 149 166
Bessel functions in stochastic processes      58Ч61 323
Bessel functions, characteristic function of      503
Beta density      50
Beta density in renewal      471
Beta integral      47
Bickel, P.J.      388
Bilateral exponential      49Ч50 502
Bilateral exponential, characteristic function of      503
Bilateral Laplace transform      434
Billingsley, P.      39 265 343
Binary orbits      33
Binomial random walks      608Ч609
Birth processes      41 266Ч267 488Ч491
Birth processes, bilaterial      491
Birth-and-death processes      479Ч483 496
Birth-and-death processes and diffusion      496
Birth-and-death processes, busy periods in      482Ч483
Bivariate normal density      70
Bizley, M.T.L.      420
Blackwell, D.      360 381
Blum, J.R.      287
Bochner integral      455
Bochner, S.      321 347 454 620 622 634 655
Bohl      268
Borel algebra      113 119
Borel algebra, measurable functions      116
Borel set      114 116 117 123 125 130
Borel set, approximation of      115 124
Borel set, convention for      127
Borel Ч Cantelli      105 317
Botts, T.A.      103
Boudreau, P.E.      196
boundary conditions      337Ч343 477
Bourbaki, N.      103
Branching processes      244 441 474Ч475
Brelot, M.      2.44
Brownian motion      99 181 322Ч349 475Ч479
Brownian motion in $R^{r}$      175 344
Brownian motion, continuity of paths in      181 332
Brownian motion, first-passage times in      174Ч175 340 476
Brownian motion, one absorbing barrier      340 477
Brownian motion, subordination of Cauchy process to      348
Brownian motion, two absorbing barriers      341 478
Brownian motion, with elastic force      335
Buehlmann, H.      229
BuffonТs needle problem      61Ч62
buses      22 55 188
Busy periods      194Ч195 198Ч200 473Ч474 482Ч483
CampbellТs theorem      179 287 595
Canonical measures      560Ч565
Cantelli      see УBorel Ч CantelliФ
Cantor distribution      35Ч36 141 593
Cantor distribution, convolutions of      146
Cantor, G.      267
CantorТs diagonal method      267Ч268
Cap and cup      104
Carleman, T.      227 515
Cauchy distribution      50 64 173 502
Cauchy distribution and random walks      204 618
Cauchy distribution and stability      173 555
Cauchy distribution in $R^{r}$      70Ч71 73 100 524 594
Cauchy distribution in Brownian motion      175 348
Cauchy distribution, bivariate      524
Cauchy semi-groups      303
Cauchy, A.      172 509
Centering      45 137 584Ч588
Centering in infinitely divisible distributions      559
Central limit theorem      258Ч265 287 291 529Ч530
Central limit theorem and large deviations      548Ч553
Central limit theorem for densities      533Ч536
Central limit theorem for equal components      515Ч518
Central limit theorem in renewal      372
Central limit theorem, applications of      209 529Ч530
Central limit theorem, expansions related to      531Ч553
Central limit theorem, with infinite variances      260
Cesaro summability      628 648
Chains, random      206Ч207
Chains, strength of      9
Chandrasekhar, S.      32
Chapman Ч Kolmogorov equations      60 334 338 346Ч347 353 566
Chapman Ч Kolmogorov equations and semi-groups      351
Chapman Ч Kolmogorov equations, continuous time      322 486Ч488
Chapman Ч Kolmogorov equations, discrete time      98
Chapman Ч Kolmogorov identity      98
Characteristic exponents of R      170
Characteristic functions      498Ч526 (see also УPoisson summationФ)
Characteristic functions in Rr      521Ч524
Characteristic functions, derivatives of      565Ч566
Characteristic functions, factorization of      506 593 631
Characteristic functions, finitely divisible      557
Characteristic functions, infinitely divisible      554Ч557 560Ч564
Characteristic functions, logarithms and roots of      554Ч555
Characteristic functions, periodic      511 626 630 631
Characteristic functions, Taylor development of      514Ч515
Chebyshev Ч Hermite polynomials      533
ChebyshevТs inequality      151Ч152 310 354
ChebyshevТs inequality for martingales      246
ChebyshevТs inequality, generalized      234
Checkerboard partitions      133
Chernoff, H.      287
Chi-square density      48
Choquet, G.      382 593
Chow, Y.S.      360
Chung, K.L.      105 167 231 355 381 483 614 615 655
Circles, covering theorem for      28Ч29
Circles, densities on      632Ч633
Circles, distributions on      29 61Ч64 627
Circles, equidistribution on      268 273
Circles, probability distribution on      274
Coin-tossing      210 211Ч212 405 417
Coin-tossing and random choice      35
Coincidences      217
Collisions of particles      206 322Ч323 325
Compactness of triangular arrays      309
Complete monotonicity      224Ч227 439Ч442 450 464
Complete monotonicity, abstract      454
Completion of measures      126
Composition of kernels      206
Compound Poisson processes      180Ч181 305 326
Compound Poisson processes and ruin problems      182Ч184 198 469Ч470
Compound Poisson processes and semi-groups      295 299Ч300
Compound Poisson processes and subordination      348Ч349
Concave functions      153
Concentration      4 45 137
Concordant functions      210Ч211 244
Conditional distributions and expectations      71Ч74 156Ч159 160Ч165
Conditional probability      157
Contagion      57Ч58
Continuity of semi-groups      353 (see also УFixed discontinuitiesФ)
Continuity theorem      431Ч433 508
Continuity theorem and Laplace transforms      433
Continuity theorem and quasi-characteristic functions of      557
Continuity theorem and semi-groups      460
Continuity theorem for densities      510
Continuity theorem, characteristic function of      508Ч509 510
Contractions      350 456
Convergence in norm = strong      257 352
Convergence in probability      253Ч254
Convergence in the mean square      636
Convergence of densities      252
Convergence of measures      247Ч252 267Ч270 284Ч285
Convergence of moments      251Ч252 269
Convergence of operators      257 285 352
Convergence, dominated      111
Convergence, notations and principles of      248Ч251
Convex functions      153Ч155
Convex functions of martingales      214Ч215
convex polygons      505
Convolution semi-groups      293Ч296
Convolutions      143Ч148 272 278
Convolutions and covering theorems      26Ч29
Convolutions and Laplace transforms      434Ч435
Convolutions of densities      7Ч8 46 71
Convolutions of singular distributions      146
Convolutions on circles      64 143 273Ч274
Convolutions, definition of      7 8
Convolutions, infinite      265Ч267 317 592Ч593
Coordinate variables      4 68
Correlation      68
Countably many intervals      108
Counters for particles      372 (see also УGeiger countersФ УQueuesФ)
Covariance      68
Covariance of processes      88Ч94 623Ч626 643Ч646
Covariance, matrix      82Ч83
Covering theorems      76 216 469
Covering theorems and convolutions      26Ч29
Cramer Ч Levy theorem      525
Cramer, H.      182 403 522 531 542 546 548 552 646 656
CramerТs estimate for ruin      182 377Ч378 403 411Ч412
Cup      104
Dams      195
Darling, D.A.      465
de Finetti, B.      179 230
decision functions      213
Decompositions      570Ч571
Defective distributions      115 129 130 205
Defective distributions in renewal      187
Degenerate distributions      83 87
Degenerate processes      90Ч91
Delayed renewal processes      187 368
Delays in traffic      190 380 387 474Ч475 496
densities      3Ч6 49Ч53 66Ч71 138Ч143
Densities, notations and conventions for      45Ч46
Denumberable sample spaces      331Ч332
Deny, J.      382
Derivatives and Laplace transforms      435
Derman, C.      493
Descending ladder variables      393Ч394
Differences, notation for      221Ч222
Differential equations, Kolmogorov      483Ч488
Diffusion processes and birth-and-death processes      496
Diffusion processes in $R^{r}$      332Ч337 344Ч345 436 461 464 475Ч479 496
Diffusion processes in genetics      336Ч337
Diffusion processes in higher dimensions      344Ч345
Diffusion processes, with elastic force      335Ч336
Digits, distribution of      34 63Ч64
Directing process      347
Directional changes of particles      323
Directions, random      29Ч33
Directly Riemann integrable functions      362Ч363
Dirichlet integral      511
Discontinuities      318
Discontinuous semi-groups      305
Discrepancies      see УEmpirical distributionsФ
Discrete distributions      55Ч58
Distance function for distributions      285
Distribution functions, definition of      3
Doblin, W.      173 592
DoblinТs УUniversal lawsФ      590Ч592
Domain of attraction      172
Domain of attraction and stable distributions      574Ч581
Domain of attraction, criteria for      312Ч316 320 448 574Ч581
Domain of attraction, normal      581
Domain of attraction, partial      320 568 590Ч592
Dominated convergence      111
Donsker, M.F.      39 343
Doob, J.L.      103 164 210 244 656
Drift in diffusion      335
Drift in random walks      397 610Ч611
Duality      394Ч398 609Ч610
Duplication formula      64
Duration of birth processes      490
Duration of busy period      473Ч474 482Ч483
Duration of dead period      190
Duration of diffusion      341Ч342
Duration of renewal process      187 216 374Ч377
Duration, estimates for      377
Dvoretzky, A.      274
Dynkin, E.B.      321 333 472 655
Economics, stable distributions in      175
Edgeworth expansion      535 542
Einstein, Albert Jr.      182 333
1 2 3 4
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