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| Ïîèñê ïî óêàçàòåëÿì |
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| Feller W. — Introduction to probability theory and its applications (Volume II) |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel summability 627 628 648
Abelian theorems 418 445
Abel’s integral equation 33
Absolute continuity 139 140
Absolute probabilities 207—209
Absolutely fair 210
Absolutely monotone functions 223—224 439 441
Absorbing barriers 340—342 464 477—479
Absorption (physical) 25 31 323
Accidents 57 181
Additive set functions 107
Additive set functions, countably = sigma 108 119 129—130
Age see “Duration”
Algebra of sets 112—113 116
Algebra of sets, generation of 163
Ambarzumian, V.A. 206 325
Anomalous numbers 63
Arc sine distributions 50
Arc sine distributions and limit theorems 470—473
Arc sine distributions in random walks 417—423
Arithmetic distributions 138 407—408
Arrays, null 177—178 585
arrays, triangular 177—178 216 308—312 583—588 596
Arzela — Ascoli theorem 270
Ascending ladder variables, strict 391
Ascending ladder variables, weak 392—393
Associated random walks 406
Astronomy, applications to 33 172 173—174 206 215 325—326
Asymptotic behavior 521 572
Asymptotic estimates 375—377 410—411
Asymptotic properties of regularly varying functions 279—284
Asymptotically dense 147
Asymptotically negligible 178
Asymptotically unbiased estimators 220
Atomic measures 137—138
Atoms (of measures) 137
Atoms (of measures), under convolutions 147 149 166
Attraction see “Domain of attraction”
Auto-regressive process 89 96
Bachelier process see “Brownian motion”
Backward equations 357
Backward equations for diffusion 334 336—337 344
Backward equations for jump processes 327—328 484—487
Backward equations for semi-groups 352 356—357
Backward equations for semi-Markov processes 497
Backward equations of Kolmogorov 327—328
Backward equations, minimal solution of 322 329—331 486
Bad luck 15—17
Baire functions 104—106 109 114 130 305 351
Banach space 257 350 487
Barriers see “Absorbing barriers” “Boundary “Reflecting
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 1 141—142
Bernstein polynomials 222—223
Bernstein polynomials in  245
Bernstein, S. 79 439
Berry — Esseen theorems 538 542—546 551
Berry, A.C. 531 536 542
Bessel density 502
Bessel functions 58—61 523
Bessel functions and infinite divisibility 177 451 566
Bessel functions and Laplace transforms 437 438 479—482
Bessel functions and related distributions 58—61 149 166
Bessel functions in stochastic processes 58—61 323
Bessel functions, characteristic function of 503
Beta density 50
Beta density in renewal 471
Beta integral 47
Bickel, P.J. 388
Bilateral exponential 49—50 502
Bilateral exponential, characteristic function of 503
Bilateral Laplace transform 434
Billingsley, P. 39 265 343
Binary orbits 33
Binomial random walks 608—609
Birth processes 41 266—267 488—491
Birth processes, bilaterial 491
Birth-and-death processes 479—483 496
Birth-and-death processes and diffusion 496
Birth-and-death processes, busy periods in 482—483
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 — Cantelli 105 317
Botts, T.A. 103
Boudreau, P.E. 196
boundary conditions 337—343 477
Bourbaki, N. 103
Branching processes 244 441 474—475
Brelot, M. 2.44
Brownian motion 99 181 322—349 475—479
Brownian motion in  175 344
Brownian motion, continuity of paths in 181 332
Brownian motion, first-passage times in 174—175 340 476
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
Buffon’s needle problem 61—62
buses 22 55 188
Busy periods 194—195 198—200 473—474 482—483
Campbell’s theorem 179 287 595
Canonical measures 560—565
Cantelli see “Borel — Cantelli”
Cantor distribution 35—36 141 593
Cantor distribution, convolutions of 146
Cantor, G. 267
Cantor’s diagonal method 267—268
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 70—71 73 100 524 594
Cauchy distribution in Brownian motion 175 348
Cauchy distribution, bivariate 524
Cauchy semi-groups 303
Cauchy, A. 172 509
Centering 45 137 584—588
Centering in infinitely divisible distributions 559
Central limit theorem 258—265 287 291 529—530
Central limit theorem and large deviations 548—553
Central limit theorem for densities 533—536
Central limit theorem for equal components 515—518
Central limit theorem in renewal 372
Central limit theorem, applications of 209 529—530
Central limit theorem, expansions related to 531—553
Central limit theorem, with infinite variances 260
Cesaro summability 628 648
Chains, random 206—207
Chains, strength of 9
Chandrasekhar, S. 32
Chapman — Kolmogorov equations 60 334 338 346—347 353 566
Chapman — Kolmogorov equations and semi-groups 351
Chapman — Kolmogorov equations, continuous time 322 486—488
| Chapman — Kolmogorov equations, discrete time 98
Chapman — Kolmogorov identity 98
Characteristic exponents of R 170
Characteristic functions 498—526 (see also “Poisson summation”)
Characteristic functions in Rr 521—524
Characteristic functions, derivatives of 565—566
Characteristic functions, factorization of 506 593 631
Characteristic functions, finitely divisible 557
Characteristic functions, infinitely divisible 554—557 560—564
Characteristic functions, logarithms and roots of 554—555
Characteristic functions, periodic 511 626 630 631
Characteristic functions, Taylor development of 514—515
Chebyshev — Hermite polynomials 533
Chebyshev’s inequality 151—152 310 354
Chebyshev’s inequality for martingales 246
Chebyshev’s 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 28—29
Circles, densities on 632—633
Circles, distributions on 29 61—64 627
Circles, equidistribution on 268 273
Circles, probability distribution on 274
Coin-tossing 210 211—212 405 417
Coin-tossing and random choice 35
Coincidences 217
Collisions of particles 206 322—323 325
Compactness of triangular arrays 309
Complete monotonicity 224—227 439—442 450 464
Complete monotonicity, abstract 454
Completion of measures 126
Composition of kernels 206
Compound Poisson processes 180—181 305 326
Compound Poisson processes and ruin problems 182—184 198 469—470
Compound Poisson processes and semi-groups 295 299—300
Compound Poisson processes and subordination 348—349
Concave functions 153
Concentration 4 45 137
Concordant functions 210—211 244
Conditional distributions and expectations 71—74 156—159 160—165
Conditional probability 157
Contagion 57—58
Continuity of semi-groups 353 (see also “Fixed discontinuities”)
Continuity theorem 431—433 508
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 508—509 510
Contractions 350 456
Convergence in norm = strong 257 352
Convergence in probability 253—254
Convergence in the mean square 636
Convergence of densities 252
Convergence of measures 247—252 267—270 284—285
Convergence of moments 251—252 269
Convergence of operators 257 285 352
Convergence, dominated 111
Convergence, notations and principles of 248—251
Convex functions 153—155
Convex functions of martingales 214—215
convex polygons 505
Convolution semi-groups 293—296
Convolutions 143—148 272 278
Convolutions and covering theorems 26—29
Convolutions and Laplace transforms 434—435
Convolutions of densities 7—8 46 71
Convolutions of singular distributions 146
Convolutions on circles 64 143 273—274
Convolutions, definition of 7 8
Convolutions, infinite 265—267 317 592—593
Coordinate variables 4 68
Correlation 68
Countably many intervals 108
Counters for particles 372 (see also “Geiger counters” “Queues”)
Covariance 68
Covariance of processes 88—94 623—626 643—646
Covariance, matrix 82—83
Covering theorems 76 216 469
Covering theorems and convolutions 26—29
Cramer — Levy theorem 525
Cramer, H. 182 403 522 531 542 546 548 552 646 656
Cramer’s estimate for ruin 182 377—378 403 411—412
Cup 104
Dams 195
Darling, D.A. 465
de Finetti, B. 179 230
decision functions 213
Decompositions 570—571
Defective distributions 115 129 130 205
Defective distributions in renewal 187
Degenerate distributions 83 87
Degenerate processes 90—91
Delayed renewal processes 187 368
Delays in traffic 190 380 387 474—475 496
densities 3—6 49—53 66—71 138—143
Densities, notations and conventions for 45—46
Denumberable sample spaces 331—332
Deny, J. 382
Derivatives and Laplace transforms 435
Derman, C. 493
Descending ladder variables 393—394
Differences, notation for 221—222
Differential equations, Kolmogorov 483—488
Diffusion processes and birth-and-death processes 496
Diffusion processes in 332—337 344—345 436 461 464 475—479 496
Diffusion processes in genetics 336—337
Diffusion processes in higher dimensions 344—345
Diffusion processes, with elastic force 335—336
Digits, distribution of 34 63—64
Directing process 347
Directional changes of particles 323
Directions, random 29—33
Directly Riemann integrable functions 362—363
Dirichlet integral 511
Discontinuities 318
Discontinuous semi-groups 305
Discrepancies see “Empirical distributions”
Discrete distributions 55—58
Distance function for distributions 285
Distribution functions, definition of 3
Doblin, W. 173 592
Doblin’s “Universal laws” 590—592
Domain of attraction 172
Domain of attraction and stable distributions 574—581
Domain of attraction, criteria for 312—316 320 448 574—581
Domain of attraction, normal 581
Domain of attraction, partial 320 568 590—592
Dominated convergence 111
Donsker, M.F. 39 343
Doob, J.L. 103 164 210 244 656
Drift in diffusion 335
Drift in random walks 397 610—611
Duality 394—398 609—610
Duplication formula 64
Duration of birth processes 490
Duration of busy period 473—474 482—483
Duration of dead period 190
Duration of diffusion 341—342
Duration of renewal process 187 216 374—377
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
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