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| Ïîèñê ïî óêàçàòåëÿì |
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| Karlin S., Taylor H.E. — A Second Course in Stochastic Processes |
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| Ïðåäìåòíûé óêàçàòåëü |
Absorbing barrier 16—18 19
Absorbing boundary 251
Absorbing state 24 29 155
Additive functional 254—255 308—313
Arcsine law 224—226 473
Attainable boundary 230
Attracting boundary 228 249
Backward equation for Brownian motion 217
Backward equation for for diffusion processes 214—216
Backward equation for for Kac functional 222—224
Backward equation for for Markov chain 143—144
Ballot problem 107 134—136
Bessel process 175—176 327 336
Bessel process, boundary behavior 238—239
Bessel process, spectral representation 338
Birth and death process 142
Boundary behavior, and infinitesimal operator 305—307
Boundary classifications 234 250
Boundary criteria 232—234
Branching process 383 384
Brownian bridge 268 269
Brownian motion 169—170 211 323 377 379 385 386 388 389 394
Brownian motion, absorbed 170 392
Brownian motion, and white noise 343
Brownian motion, arcsine law 224—226
Brownian motion, backward equation 217
Brownian motion, boundary behavior 228—229 230 236
Brownian motion, compounded 378
Brownian motion, conditioned process 267—272 388
Brownian motion, control problem 212
Brownian motion, geometric 175 359—360 380
Brownian motion, infinitesimal operator 289 297
Brownian motion, instantaneous return process 261
Brownian motion, n-dimensional 291—292 299 312—313 380 382 393
Brownian motion, radial process 335—336
Brownian motion, reflected 170 327 337 379 392
Brownian motion, resolvent 288
Brownian motion, spectral representation 337 393
Brownian motion, standard 197 205
Brownian motion, with drift 205
Busy period 513—519
Cash inventory model 211—212
Chapman — Kolmogorov equation 286
Compound Poisson process 426—440
Compound Poisson process, decomposition of 433—436
Compound Poisson process, sum of 430—431
Conditional diffusion process 261—272 387
Conditional diffusion process, boundary behavior 263—264
Conditional diffusion process, Green function 264—265
Conservative diffusion 161
Conservative process 143
Convergence to diffusions 168
Coupling 93
Differential operator 388
Diffusion coefficient 159
Drift coefficient 159
Dynamical systems 343—345
Dynkin condition 163 165
Dynkin formula 297—299 308—313
Dynkin formula, applications 299
Ehrenfest urn model 171
Elastic boundary 255—257
Empirical distribution 113—116 119—123
Entrance boundary 235 246 382
Entrance boundary, stationary distribution 241—242
Excessive function see “Superregular sequence”
Exchangeable random variables 454 516
Exit boundary 233—234 246
Exit time 302—303
Feller property 291
Forward equation for diffusion processes 219
Forward equation for Markov chain 143 144
Fundamental matrix 24
Gene frequency model 177 206—208 361—362 381 387 390
Gene frequency model, boundary behavior 239—241
Gene frequency model, spectral representation 336—337
Gene frequency model, with mutation 177—179 180—183 208—211 239—241 265—266
Gene frequency model, with mutation and selection 222
Gene frequency model, with selection 180 184—188
Genetic recombination 272—284
Green function 198—202 287
Green function, and resolvent operator 293
Green function, for Brownian motion 205
Harmonic function see “Regular sequence”
Hewitt — Savage 0—1 law 477
Hille — Yosida theorem 296
Hitting time 158 162 192 226
Hitting time of boundary 228 242—243
Infinitesimal generator 286
Infinitesimal matrix 145
Infinitesimal mean 159
Infinitesimal operator 195 287 294—295
Infinitesimal operator, and boundary behavior 305—307
Infinitesimal operator, as differential operator 303—305
Infinitesimal operator, domain of 307—308
Infinitesimal operator, Dynkin form 300—302
Infinitesimal parameters 159
Infinitesimal variance 159
Input distribution 489
Instantaneous return process 260—261
Instantaneous state 147
Interchangeable 108—113
Ito integral 346—347 356—357
Ito transformation formula 173 347—348 371—372 389
Ito transformation formula, applications 374—375
Jacobi diffusion 335
Jump boundary 258—260
Kac functional 222—224 313—316 393
Killing rate 204 313—316
Killing time 161 382
Killing time, example 272—284
Kolmogorov condition 465
Ladder index 95
Ladder random variable 464—465 480
Levy process 319 432—433
Lightning model 446
Local time 198 207 251—253 316—324
Local time, inverse of 317—318
Logistic equation 360—361
Markov time 149—150
Martingale 167 308—312 325—327 371 376—377 382
Martingale and stochastic integrals 352—355
| Maximum random variable 451 463 483—484 486
Minimal process 148
Multiplicative functional 313—316
Mutation see also “Gene frequency model”
Mutation in population 188—191
Natural boundary 235—236 246
Natural scale 196
Occupation time 252 452
Optimal allocation model 367—368
Optimal growth model 366—367
Optimal stopping 50—64 68—69
Option price model 365—366 389
Order statistics 100—107 124 125 129
Ornstein — Uhlenbeck process 170—173 183 345—346 379 380
Ornstein — Uhlenbeck process, backward equation 218
Ornstein — Uhlenbeck process, boundary behavior 237
Ornstein — Uhlenbeck process, in n dimensions 292
Ornstein — Uhlenbeck process, radial process 333—334
Ornstein — Uhlenbeck process, spectral representation 332—333
Ornstein — Uhlenbeck process, stationary distribution 221
Periodic class 6—10 78
Poisson point process see also “Poisson process”
Poisson point process, spatial 436—440
Poisson process and uniform distribution 403 404
Poisson process in astronomy 404—405
Poisson process, spatial 398—403 441 443 445
Population growth model 188—191 354—355 358 378 382 383 390
Population growth model, boundary behavior 239
Population growth model, geometric 413—416
Population growth model, in space and time 416—419
Population growth model, spectral representation 334
Population growth model, two types 444
Population growth model, with age structure 419—426
Population growth model, with immigration 405—408
Population growth model, with mutation 408—413
Production and consumption model 363—365
Progressively measurable 369
Quasi-left continuity 163
Queue discipline 489
Queueing process 394
Queueing process,  506—510
Queueing process,  522
Queueing process,  449 521 522
Queueing process,  519—520
Queueing process, embedded Markov chain 497—503
Queueing process, G/M/1 504—506
Queueing process, GI/G/1 524
Queueing process, GI/GI/1 492—496
Queueing process, GI/M/s 511—513
Queueing process, M/G/1 523
Queueing process, M/GI/1 497—503
Queueing process, M/M/l 490—492 519 520 524
Queueing process, M/M/s 519
Queueing process, notation 490
Queueing process, with balking 520—521
Quiz show 56—58
Radial Brownian motion see “Bessel process”
Random time change 253—255
Random walk 25 26 67 82 97 98 99
Random walk, optimal stopping 58—59
Random walk, spectral representation for 10—23
Recurrence 72—76 83 153 155
Recurrence, criterion for 73
Recurrent class 9 23 35
Recurrent Markov chain 3—4 65 66
Recurrent Markov chain, criterion for 37—40 47 49
Recurrent state 34
Reflecting barrier 14—16
Reflecting boundary 251
Regular boundary 232—233
Regular diffusion 158
Regular sequence 44—45 83
Renewal Theorem 93—95
Renewal theory 482
Resolvent operator 287 292—294
Reversed process 42 69
Scale function 194 226
Scale measure 227
Semigroup theory 305
Semigroup theory for Markov processes 285—294
Service distribution 489
Shock model 429—430
Signal detection model 368
Spectral representation, for absorbed Brownian motion 393
Spectral representation, Jacobi diffusion 335
Spectral representation, Markov chain 5 23
Spectral representation, matrix 1—3
Spectral representation, Ornstein — Uhlenbeck process 332—333
Spectral representation, population growth model 334
Spectral representation, random walk 14—18
Speed density 195 197
Speed measure 195 227
Spitzer’s identity 460 472
Stable state 146
Standard process 162
Standard transition function 138
Stationary distribution 220—221 236 241—242 386
Stationary distribution, generalized 37 42—43
Sticky boundary 257—258
Stochastic differential equation, solution of 373—374
Stopping rule problems see “Optimal stopping”
Stratonovich integral 346—347 351 353—354 356—358 390—391
Strength model 439—440
Strong Markov property 149—152
Subadditive function 139
Subregular sequence 44—45
Superregular functions, transient Markov chains 47
Superregular majorant 56 59—62
Superregular sequence 44—45 52—53 66
Taboo probabilities 31—32
Total positivity 167
Transience 75
Transient class 24
Transient Markov chain 67
Trap state 378
Unattainable boundary 230
Virtual waiting time 513—519
Warrant price model see “Option price model”
White noise 342—343
Wong — Zakai integral 348—351
Wright — Fisher model see “Gene frequency model”
wronskian 200
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