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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 |
Lukacs, E. 86 655
Lundberg, F. 182
Mandelbrot, B. 175 288
Marginal distribution 67 134 157
Marginal distribution, normal 100
Marginal distribution, prescribed 165
Markov processes with continuous time 96 321—345 624—625 “Semi-Markov
Markov processes with continuous time and ergodic theorems 369 491—492
Markov processes with continuous time and semi-groups 349—357 454—458
Markov processes with continuous time in countable spaces 483—488
Markov processes with discrete time 94—99 101—102 205—209 217
Markov processes with discrete time and ergodic theorems 270—274
Markov processes with discrete time and martingales 244
Markov processes with discrete time and spectral aspects 635 649
Markov property 8—9
Markov property, strong 20
Markov, A. 228
Marshall, A.W. 246
Martingales 209—215 241—244
Martingales, inequalities for 241—242 246
Matrix calculus 82—83 484—485
Maximal partial sums 198 402 408—412 419—423
Maximal partial sums, estimate of 412
Maximal recurrence time 189 386
Maximal row sums 320 597
Maximal term 172 277 287 465 “Record
Maxwell distribution 32 48 78—79
Mc Kean, H.P.Jr. 333 655
Mc Shane, E.J. 103
Mean approximation theorem 111—112
Mean square convergence 636
Mean value theorem 109
Measurability 113—115
Measure space 115
Median 17 137
Metrics for distributions 285 (see also “Banach space” “Hilbert
Microscopes 31
Middleton, D. 631
Milky Way brightness 325
Miller, H.D. 603
Mills, H.D. 101
Minimal solutions and diffusions 339
Minimal solutions and jump process 329—331
Minimal solutions and semi-Markov processes 497
Minimal solutions and W1Ener — Hopf equation 402
Minimal solutions of Kolmogorov differential equations 485—488
Mirror experiment 51
Mittag — Leffler function 453—454
Mixtures 53—55 73 159 167
Mixtures and transforms 437 504
Moments 5 136 151 570
Moments and derivatives 435
Moments in renewal 375
Moments, convergence of 251—252 269
Moments, generating function 434
Moments, Hausdorff moment problems 224—228 245
Moments, inequalities 155
Moments, uniqueness problem 227 233 514—515
Moments, uniqueness problem, in  529
Monotone convergence principle 110
Monotone convergence principle, property of 350—352
Monotone functions 275—277
Monotone sequences 105
Mortality, random walks with 424
Moving average processes 88—89 645
Muentz, H.Ch. 245
Multivariate normal characteristic functions 522—523
Natural scale in diffusion 333
nearest neighbors 10
Needle problems, Buffon’s 61—62
Nelson, E. 100 347
Neumann, J.V. 44
Neumann, K., identity of 60
Neveu, J. 103 655
Newell, G.F. 40
Neyman, J. 182
Nikodym see “Radon — Nikodym” “Lebesque
Noise see “Shot effect”
Nonlinear renewals 387
Norm 256 350 636 642
Norm, topology 286
Normal distributions 46 64 87 173 503 566
Normal distributions in 83—87 522
Normal distributions, bivariate 70 72 101
Normal distributions, characterization of 77—80 85 525—526
Normal distributions, degenerate 87
Normal distributions, domain of attraction 313 577—578
Normal distributions, marginal 99—100
Normal distributions, Markovian 94
Normal semi-groups 299 307 319
Normal stochastic processes 87—94 641—646
Nucleons 323
Null arrays 177—178 583—588
Null sets 125—126 140
Nyquist, N. 631
Operational time 181 345
Operators associated with distributions 254—258
Optional stopping 213
Orbits, binary 33
Order relation in 82 132
Order statistics 18 20—21 100
Order statistics and limit theorems 24 43
Order statistics, application to estimations 41
Orey, S. 381
Ornstein — Uhlenbeck process 99 335—336
Oscillating random walks 204 395
Osipov, L.V. 545
Paradoxes 11—14 23 187
Pareto distribution 50 175
Parseval relation 463 507 615 619—620 638 641 644
Parseval relation as Khintchine criterion 639—640
Partial attraction 320 568 590—592
Partial ordering 82 132
Particles, collisions of 206 322—323 325
Particles, counters for 372
Particles, directional changes of 323
Particles, energy, losses of 323 325
Particles, splitting of 25 42 100
Patients, scheduling of 183
Pearson, K. 48
Pearson’s system of distributions 48 50
Pedestrians 189 378 387
Periodograms 76
Persistency see “Transient distributions”
Petersburg game 236
Petersen, D.P. 631
Petrov, V.V. 545 552
Phillips, R.S. 231 294 454 656
Pinkham, R.S. 63
Pitman, E.J.G. 565
Plancherel theorem 510
Plancherel transform 637—640
Planck see “Fokker — Planck”
Platoon formation 40
Poincare, H. 62
Poincare’s roulette problem 62—63
Point functions 128
Poisson distributions 566
Poisson distributions, approximations by 286
Poisson distributions, compound 555 557—558
Poisson distributions, difference of 149 166 567
Poisson ensembles 15 (see also “Gravitational fields”)
Poisson kernel 627 648
Poisson processes 12 14—15 “Pseudo-Poisson
Poisson processes as limit in renewal 370
Poisson processes, direction of by gamma process 348—349
Poisson processes, direction of gamma process by 349
Poisson processes, gaps in 378
Poisson processes, supremum in 183
Poisson’s summation formula 63 343 629—633 648
| Polar coordinates 68
Pollaczek, F. 198 (see also “Khintchine — Pollaczek”)
Pollak, H.O. 217
Pollard, H. 360 381
Polya distribution 57
Polya’s criterion 505 509
Polya’s urn 210 229—230 243
Polymers 206
Population growth 337
Population growth, logistic 52—53
Population growth, random dispersal of 261—262
Port, S.C. 279
Positive definite functions 620—623
Positive definite matrices 81
Positive definite sequences 633—635
Positive variables 571—572
Potentials 488
Power spectrum 624
Prabhu, N.U. 656
probability density see “Densities”
Probability distributions 130
Probability distributions in 127—165
Probability measures and spaces 103—116 133
Processes with independent increments 179—184
Product measures and spaces 121—123
Prohorov, Yu.V. 39 343
Projection 67
Projection of random vectors 30 32 33
Proper convergence 248 285
Proper distributions 130
Pseudo-Poisson processes 322—324 345
Pseudo-Poisson processes and exponential formula 354
Pseudo-Poisson processes and semi-groups 354—357 459
Pseudo-Poisson processes with linear increments 324—325
Pure birth process 488—491
Pyke, R. 183 389 470 497
Quasi-stable distributions 173
Queues 54—55 65 196—197 208 481—482
Queues and limit theorems 380
Queues and paradoxes 12—14
Queues for shuttle trains 196—198
Queues, joint distribution for residual and spent waiting times 386
Queues, one-server 194—195
Queues, parallel 17 18 41
Queuing processes 194—200 208 380 410
Radiation, stellar 206
Radon — Nikodym derivative 139
Radon — Nikodym theorem 139 140 141
Raikov’s theorem 571
Random chains 206—207
Random choice 2 21—25 69
Random choice and coin tossing 35
Random directions 29—33 42 43 142
Random directions, addition of 31—33 207 523
Random dispersal 261—262
Random flights 32—33
Random partitions 22—23 74—75
Random splittings 25—26 42 100
Random sums 54 159 167 504
Random sums, central limit theorems for 265 530
Random sums, characteristic function for 504
Random variables 4 68 116—118 131
Random variables, complex 499
Random vectors 31 33 107—108
Random walks in  190—193 200—204 389—425 598—616 “Ladder
Random walks in , associated 406
Random walks in , empirically distributed 38
Random walks in , simple ( = Bernouilli) 213—214 318 393 395 425 437
Random walks in 32—33
Random walks in , central limit theorem for 261
Randomization 53—64
Randomization and exchangeable variables 228
Randomization and semi-groups 231 355
Randomization and subordination 345—349
Randomized random walks 58—61 479—483 566—567
Ratios 16—17 24—25 54
Ray, D. 333
Rayleigh, Lord 32—33 523
Record values 15—16 40
Rectangular density 21 50
Recurrence time 184
Recurrence time, maximal 189 386
Recurrence time, observed 13 187
Recursive procedures 26
Reflecting barriers 340 343 464
Reflection principle 175 477 478
Regeneration epochs 184
registrations 191 373
Regression 72 86
Regular stochastic kernels 271—273
Regular variation 275—284 288 289
Reliability theory 52
Renewal epochs 184 372—374
Renewal equation 185—187 359 366—368 385—388
Renewal equation, theory of 466—468
Renewal processes 12 184—187 216 358—388
Renewal processes, applications of 377—378
Renewal processes, imbedded 191—193
Renewal processes, nonlinear 387
Renewal processes, superposition of 370—371
Renewal processes, transient 374—377
Renewal processes, two-stage 380
Renewal theorems 358—372
Renewal theorems on the whole line 201 380—385 428
Renewal theorems, proof of 364—366
Renyi, A. 343
Reservoirs 182 183 195
Residual waiting time 188
Residual waiting time, limit theorem for 369 370 386 471—472
Resolution of identity 643
Resolvents 429 452—453 455 487
Resolvents and complete monotonicity 461
Resultant of random vectors 31 146 523
Returns to the origin 424
Richter, W. 552
Riemann integrable, directly 362—363
Riemann — Lebesque theorem 513—514 538 629
Riesz, F., representation theorem of 120 134 251
Riesz, M. 231
Riordan, J. 656
Risk theory 182—183 (see also “Ruin problems”)
Robbins, H.E. 99 265 360
Rosenblatt, M. 77 287 656
Rotational symmetry 523—524
Rotations 78 84 101
Rouche’s Theorem 408
Roulette 22 62
Rounding errors 22 62
Row vectors 83
Royden, H.L. 228
Ruin problems 198 326
Ruin problems in compound Poisson processes 182—184 469—470
Ruin problems, estimates for 377—378 411—412
runs see “Record values”
Rvageva, E.L. 39
Sample extremes and median 18
Sample mean and variance 86—87
Sampling theorem 631—632 633
Sankhya 571
Savage, L.J. 124 229
Scale parameters 45 134
Scheduling of patients 183
Schelling, H.v. 208
Schloemilch’s formula 60 566—567
Schmidt, R. 445
Schwarz’ inequality 152—153 166 498 527 642
Second moments 5
Selection theorems 267—270
Self-reciprocal functions 503
Self-renewing aggregates 187’
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