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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 |
Elastic forces 335—336
Electric transmission lines 208—209
Empirical distributions 36—39
Empirical interpretations 22
Endomorphisms 350
Energy losses 25 323
Ensembles of circles and spheres 9—10
Ensembles, random, of points in space 9
Entrance probability see “Hitting points”
Equicontinuity 252 270
Equidistribution theorem 268
Equivalent functions 125 636 642
Erdoes, P. 343 360
Ergodic limits 491—493
Ergodic stochastic kernels 271
Ergodic theorems 270—274 491
Esscher, F. 552
Esseen, G. 540 542 544 545
Estimator 41
Exchangeable variables 228—230 423
Exchangeable variables, central limit theorem for 287
Expansions and the central limit theorem 531—553
Expansions for distributions 538—542
Expansions, involving varying components 546—548
Expectations 117—118 133
Expectations, conditional 162—165
Expectations, definition of 5
Explicit expressions 193
Exponential distributions 1 8—21 39—43 74—77
Exponential distributions and uniform distributions 44 74—77
Exponential distributions as limits 24 43 370
Exponential distributions, bilateral 49 148
Exponential distributions, bivariate 100
Exponential distributions, reduction to 25—26
Exponential formula of semi-groups 231 353—355
Extension theorem 118—121 123
Fair, absolutely 210
Fatou’s theorem 110—111 636
Fatou’s theorem for boundary values 244
Fejer, L. 628
Feller, W. 53 61 179 194 262 279 289 325 331 333 337 360 381 430 483 496 497 546 552 581
Filters 88 625
Finetti, B. de 42 179 230
Finite arithmetic distributions 608—609
First entry see “Hitting points” “Ladder
First passages and Markov chains 492
First passages in diffusion 174—175 340—341 475—476
First passages, birth-and-death processes 60—61 481 494—495
First return 391 424 495
Fisher, R.A. 77 277 336
Fisher’s Z-statistic 49
fishing 182
Fixed discontinuities 324—326 328
Fokker — Planck equation 296 323 324 325 328
Forward equations 337—343 484
Forward equations and diffusion 337—343 475—479
Forward equations and jump processes 324 .328
Forward equations and semi-groups 352
Forward equations of Kolmogorov 324 328
Forward equations, minimal solution for 329 331—332 485—488
Fourier analysis, applications of to random walks 598—616
Fourier coefficients 628 634 647—648
Fourier inversions 509—510 511 639
Fourier series 626—629 641
Fourier transforms 499 532
Fourier — Stieltjes transform 499 606
fractional parts 148 268
Frechet’s maximal distribution 166
Free paths 10—11
Frequency functions, definition of 8
Fubini’s Theorem 111 122 144
Fuchs, W.H.J. 614 615
Functional, linear 120
Galton, F. 73
Gamma distributions 11 47—48 176 435 502 503
Gamma distributions, alternate name for 48
Gamma distributions, approximation by 220
Gamma distributions, infinitely divisible 176 451 567
Gamma distributions, limit of order statistics 24
Gamma distributions, randomized 58—59
Gamma distributions, subordination 336—337
Gamma functions 47
Gamma process, direction of by Poisson process 349
Gamma process, direction of by Poisson process, direction of Poisson process by 348—349
Gaps, large 188 378 468
Gaps, small 217
Geary, R.C. 86
Geiger counters 189 190 372—373 387 468
Generating functions, characterization of 223
Generating functions, mortality interpretation for 424
Generation of algebras 163
Generation of exponentially distributed variables 44
Generators 294—296 356—357 456—457 476
Genetics, diffusion in 336—337
Gilbert, E.N. 217
Gnedenko — Koroljuk theorem 43
Gnedenko, B.V. 38 39 277 531 540 581 592 656
Good, I.J. 473
Gravitational fields 173—174 215
Green function 334 476 496
Greenwood, M. 57
Grenander, U. 77 655 656
Griffin, J.S., Jr. 196
Grouping of data 4—5
Growth, logistic 52
Gumbel, E.J. 165
Hadamard’s factorization theorem 525
Halmos, P.R. 103 213
Hamel equation 298 305
Hardy, G.H. 155 268 445
Harmonic analysis 619—646
Harmonic functions 244
Harris, T.E. 244
Hausdorff, F. 226
Height distribution 73
Heitler, W. 323
Helly, E. 267
Hennequin, E. 103
Herglotz, G. 634
Hermite polynomials 523—533 535
Hermite polynomials, expansion of 542
Hewitt, E. 124 229
Heyde, C.C. 227
Hidden periodicities 76
Hilbert spaces 271 637 639—643 645
Hille — Yosida theorem 458—463 476
Hille, E. 231 294 408 454 525 656
Hitting points see “Ladder variables”
Hitting points in random walks 426 598—599
Hitting points in renewal 188 371—372 426
Hobby, C. 389
Holder’s Inequality 155
Holtsmark distribution 172 173—174 215
Hopf, E. 403 (see also “Wiener — Hopf”)
Hunt, G. 210
Huygens’ principle 51
Hyperbolic functions and densities 502—503 527 567 632—633
Ibragimov, I.A. 167
Idle servers 200
Images, method of 340
Imbedded renewal processes 191—193 379
Improper see “Proper distributions”
Increase, point of 137 147
Independence of random variables 6 69 71 121—125 134
Independence of random variables and complex variables 498
Independence of random variables, criterion for 136
Independent increments 95—96 179—182 293 304 317 645
Independent increments and discontinuities 305 317—318
Independent increments and subordination 347
Index of the first maximum 417
| Indicators 104
Induced partitions 22
Induced random walks 390
Inequalities 152—156
Inequalities of Hoelder 155
Inequalities of Jensen 153—154
Inequalities of Kolmogorov 156
Inequalities of Schwarz 152—153
Inequalities, moment 155
Infinite convolutions 265—267 317 592—593
Infinite differentiability 256 293
Infinitely divisible distributions 176—179 292—293 449—452 554—595
Infinitely divisible distributions and semi-groups 290—318 457—458
Infinitely divisible distributions in  593 596
Infinitely divisible distributions, special properties of 570—574
Infinitesimal generators 456
Infinitesimal speed and variance 335
Inner products 636
Inspection paradox 187 372
Insurance see “Risk theory”
Integrals, stochastic 645—646
Integration by parts 150—151
Integration by parts and Laplace transforms 435—436
Interval functions 106—112 128 129
Interval of continuity 248
Invariance principle 343
inventories 195—196
Inversion formulas 140 221—222 638
Inversion formulas and moment problems 227
Inversion formulas for Laplace transforms 232—234 440—441 462
Inversion formulas, characteristic functions for 510—511 524
Ionization 323
Isometry 638
Ito, K. 333 655
Jacobi’s theta functions 342 345 632
Janossy, L. 323
Jensen’s Inequality 153—154 214
Joint distributions 68 423—425
Jordan decomposition 138 142
Joseph, A.W. 420
Jump processes 326—332
Jump processes, with infinitely many jumps 331 484
Kac, M. 79 196 343
Karamata, J. 173 247 275 279 445
Karlin, S. 228 381 656
Katz, M.L. 545
Kelvin; Lord 340
Kemperman, J.H.B. 655
Kendall, D.G. 194 231 473
Kernels, stochastic 159 205 270—272
Khintchine A. 137 173 179 406 527 565 588 592 639—640 656
Khintchine — Pollaczek formula 410 470 617
Khintchine’s criterion 639—640
Khintchine’s law of large numbers 235 436
Khintchine’s unimodality criterion 158 527
Kiefer, J. 200
Kingman, J.F.C. 184
Kolmogorov — Smirnov theorem 39 342—343
Kolmogorov, A.N. 39 123 124 179 325 333 531 540 656
Kolmogorov’s backward equation 327 328
Kolmogorov’s differential equations 331 483—488
Kolmogorov’s forward equation 324 328
Kolmogorov’s inequality 156 246
Kolmogorov’s inequality for martingales 242
Kolmogorov’s inequality for positive submartingales 241—242
Kolmogorov’s three-series theorem 317
Koroljuk, V.S. 33 38 39 43
Krickeberg, K. 103 655
Kronecker delta kernel 206 484
Kronecker’s lemma 239 243
Ladder epochs, distribution of 413—417
Ladder heights 191 398—400
Ladder indices 412—413
Ladder points 390
Ladder variables, ascending, strict 391
Ladder variables, ascending, weak 392—393
Ladder variables, descending 393—394
Laha, R.G. 655
Lamperti, A. 189
Landau, E. 342 446
Landau, L. 323
Laplace transforms 232—233 429—458
Laplace transforms and convolutions 434—435
Laplace transforms and derivatives 435
Laplace transforms and integration by parts 435—436
Laplace transforms and moments 435
Laplace transforms and random walks 614
Laplace transforms for semi-groups 454—458
Laplace transforms in 452—454
Laplace transforms, applications of 466—495
Laplace transforms, elementary properties of 434—436
Laplace transforms, examples of 436—439
Laplace transforms, inversion formulas for 232—234
Laplace — Stieltjes transform 432 470 495 496
Laplace’s second law 50
Last come first served 190
Lattice distributions 138 (see also “Poisson’s summation formula”)
Lattice distributions, central limit theorem for 517—518 540
Lattice distributions, characteristic functions for 511
Lattices (algebraic) 350
Law of Large Numbers 219—246 286 436 513
Law of large numbers for identically distributed variables 234—237
Law of large numbers for stationary sequences 245
Law of large numbers for triangular arrays 316—317 596
Law of large numbers, converse 241
Law of large numbers, Khintchine’s law 235
Law of large numbers, strong law 237—241
Law of large numbers, weak law 235—236
Le Cam, L. 286
Lebesque completion 126
Lebesque decomposition theorem 142
Lebesque measure 33—36 126
Lebesque — Nikodym theorem 140 (see also “Riemann — Lebesque theorem”)
Lebesque — Stieltjes integral 110 119 121 131—132
Leffler see “Mittag — Leffler”
Legendre’s duplication formula 64
Length of random chains 206—207
Levy — Pareto distribution 172 (see also “Pareto distribution”)
Levy, P. 173 179 181 210 262 274 285 305 314 318 497 515 525 565 567—568 571 575 588 592 655 656
Levy’s canonical measure 564
Levy’s examples 215 319 567—568
Levy’s metric 285
Lifetime see “Duration” “Recurrence
Light in stellar systems 206 325—326
Light, absorption of 31
Light, Huygens’ principle of 51
Light, intensity of 25
Light, transmission of through matter 25 31 43
Likelihood ratios 211
Limit theorems 24 342—343
Limit theorems and arc sine distributions 470—473
Limit theorems and queues 380
Limit theorems, basic 247—288
Lindeberg conditions 262 263 286 518—521 530
Lindeberg conditions in diffusion 333
Lindeberg.J.W. 515
Lindley, D.V. 194 389
Linear functional 120
Linear increments in jump processes 324—326
Linear operators on stochastic processes 625—626
Little, J.D.C. 474
Littlewood, J.E. 155 445
Ljapunov’s condition 286
Locally compact spaces 120 123 248
Locked period 189
Loeve, M. 103 104 229 .265 321 655
Logarithmic distribution 63
Logistic distribution and growth 52—53
Lost calls 190 495.
Luck, persistence of 15—17
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