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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 |
Semi-groups 231—232
Semi-groups and infinitely divisible distributions 290—318
Semi-groups and Laplace transforms 454—458
Semi-groups and Markov processes 349—353
Semi-groups, Cauchy 303
Semi-groups, compound Poisson 299—300
Semi-groups, convolution 293—296
Semi-groups, discontinuous 305
Semi-groups, exponential formula of 353—355
Semi-groups, generators of 356—357
Semi-groups, normal 299
Semi-groups, stable 305—308
Semi-groups, with finite variances 298—300
Semi-Markov processes 483 497
Semi-martingale 214
Separability 269
Servers see “Queues” “Queuing”
Servo-stochastic process 101—102
Servomechanisms 101—102
set functions 106—107
Sets, algebras of 112—113
Sets, null 125—126
Shannon, C. 631
Shapiro J.M. 571
Shepp, L. 64 158 618 648
Shift operator 643
Shohat, J.A. 228 245
Shot effect 178—179 287 595
Shuttle trains 196
Sierpinski, W. 268
Sigma additive 108
Sigma algebras 112—113
Sigma finite measures 115
Significance test 76—77
Significant digits 63
Simple conditional distributions 156—159
Simple functions 131
Singular distributions 36 107—108.141
Singular distributions, convolutions of 146 593
Skellam, J.G. 262
Skitovic, V.P. 79
Skorokhod, A.V. 39 655
Slow variation see “Regular variation”
Smirnov, N.V. 39 43
Smith, W.L. 363 381 497
Smoothing 88 144 536—538
Snedecor’s density 49
spaces 115—125
span 138
Sparre-Andersen transformations 421—422
Sparre-Andersen, E. 389 413 418—423
Special densities 45—53
Spectral measure 624 647
Spectral measure, prescribed 626
Spectral theorem for unitary operators 643
Speed measure 333
Spent waiting time 188 386
Spent waiting time, limit theorems for 371 471
Spheres, passage through 30—31
Spheres, passage through, uniform distribution on 69
Spitzer, F. 198 389 404 418 605 612 618 655
Splittings, random 25—26
Stable distributions 169—176 574—581 “Domain
Stable distributions in  594 597
Stable distributions in renewal 373
Stable distributions of order  52 64 173 319 436—437
Stable distributions, densities of 581—583
Stable distributions, positive 448—449
Stable distributions, products of 176 452
Stable distributions, strictly stable 170
Stable distributions, subordination 348 451
Stable distributions, symmetric 172
Stable semi-groups 305—308
Stages in rivers 182
Stars, gravitational field of 173—174 215
Stars, gravitational field of, neighbors of 10
Stars, gravitational field of, radiation from 206 325—326
Stationary increments 180 293
Stationary measure and probability 208 272
Stationary processes 87—94 101 623—626 “Steady
Stationary processes, law of large numbers for 245
Stationary sequences 97—98
Statistic 18
Steady-state 14 207—208 326
Steady-state in renewal 370 386
Stein, C. 601
Step functions 108
Steutel, F.W. 452
Stevens, W.L. 77
Stieltjes 228 (see also “Lebesque — Stieltjes integrals” “Laplace
Stirling’s formula 47
Stochastic boundedness 254 309
Stochastic difference equation 90
Stochastic integrals 645—646
Stochastic kernels 159 205 270—272 349 351
Stochastic processes 304—305 641—646
Stochastic processes, limits in 379—380
Storage and inventories 195—196 (see also “Reservoirs”)
Stratification 57
Strength, tensile 9
Strict sense stable 170
Strong continuity of semi-groups 454
Strong convergence 257 350
Strong Law of Large Numbers 237—241
Studden, W. 228 656
Student’s density 49
Sub martingale 214 241—242
Subordination of processes 345—349 355 451—452 458 573—574 596
Substochastic kernels 205
| Superposition of renewal processes 370
Support 45
Symmetric Cauchy distribution in 70—71
Symmetric Cauchy distribution in  71
Symmetric distributions 172 526
Symmetric events 124
Symmetrically dependent variables = Exchangeable variables 228—230
Symmetrization 148—150
Symmetrization inequalities 149
Systems, impossibility of 213
Tail events 124
Takacs’ integral equation 473
Tamarkin, J.D. 228 245
Tanner, J.C. 189
Tauberian theorems 363 442—448
Tauberian theorems, applications of 418 419 448 467 471 612—614
Taylor development 512 514—515 528
Taylor expansion 585 616
Taylor formula 312
Taylor formula, generalized 230—231
Taylor series 534 536
Teicher, H. 287
telephone calls 57 179
Telephone calls, lost calls 190 495—496
tensile strength 9
Terminating ( = Transient) renewal processes 186—187 374—377
Theta functions 343 632
Three-series theorem 317
Titchmarsh, E.C. 613
Tortrat, A. 103 593
Total variation 286
Traffic problems 40 189 378 387 474—475 496
Trains, queues for 196—198
Transient ( = Terminating) renewal process 186—187 374—377
Transient distributions 614—616
Transient random walks 201—204
Transient random walks, criteria for 203 415 614—616 618
Transient random walks, renewal equation and theorem for 200 384 428
Transition operators 350
Translation operator 231—232 256
Translation principle 432
Translation semi-groups 295 357
Transmission lines 208—209
Trees, growth of seeds of 261—262
Triangle inequality 256
triangular arrays 177—178 216 308—312 583—588 596
Triangular density 26 50 502 503
Trotter, H.F. 262
Trunklines see “Telephone calls”
Type of distribution 45 137
Uga herit 217
Uhlenbeck see “Ornstein — Uhlenbeck”
Unbiased estimator 220
Uniform distribution 21—29 50 502 503
Unimodal distributions 158 527
Unimodal distributions, convolutions of 164
Unitary operators in Hilbert space 643
Vacuum tube 178—179 287 595
Vanishing at infinity 248
Variable distributions 316—318
Variables, independent, sequences of 123—125
Variables, random 116—118
Variance 5 46 136
Variance, conditional 72
Variance, infinitesimal 335
Variation, total 286
Vector notation 82
Velocities, Maxwell distribution for 32 48 78—79
Violins, loudness of 31
Visibility 10
Visits in random walks 191 202
von Neumann, J. 44
von Schelling, H. 208
Waiting lines see “Queues”
Waiting time paradoxes 11—14 372
Waiting times 17—20
Wald, A. 228 397 406
Wald’s identity and approximations 401 426 427 428 601—604
Wallace, D.L. 542
Walsh, J.W. 51
Wax, N. 656
Weak convergence 251
Weber, H. 438
Weibull distributions 52
Weierstrass approximation theorem 223
Weyl, H. 268
Whittaker, J.M. 631
Wiener process see “Brownian motion”
Wiener — Bachelier process 181
Wiener — Hopf factorization 389 400—402 428 604—609 617
Wiener — Hopf integral equation 402—404 406 425
Wiener — Hopf techniques 412
Wiener — Khintchine criterion 640
Wiener, N. 305 363 403 640
Wilks, S.S. 40
Wintner, A. 167
Wold, H. 522
Wolfowitz, J. 200 274 381
Wright, E.M. 268
Wright, S. 336
Yaglom, A.M. 656
Yahav, J.A. 388
Yosida, K. 321 656
Yule, G.U. 57
Zero-or-one laws 124
Zolotarev, V.M. 583
Zygmund, A. 565
“Normal” domain of attraction 581
“Universal laws” of Doblin 590—592
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