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Karlin S., Taylor H.E. Ч A Second Course in Stochastic Processes
Karlin S., Taylor H.E. Ч A Second Course in Stochastic Processes

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Ќазвание: A Second Course in Stochastic Processes

јвторы: Karlin S., Taylor H.E.

јннотаци€:

This Second Course continues the development of the theory and applications of stochastic processes as promised in the preface of
A First Course. We emphasize a careful treatment of basic structures in stochastic processes in symbiosis with the analysis of natural classes of stochastic processes arising from the biological, physical, and social sciences.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 1st edition

√од издани€: 1981

 оличество страниц: 542

ƒобавлена в каталог: 12.02.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Absorbing barrier      16Ч18 19
Absorbing boundary      251
Absorbing state      24 29 155
Additive functional      254Ч255 308Ч313
Arcsine law      224Ч226 473
Attainable boundary      230
Attracting boundary      228 249
Backward equation for Brownian motion      217
Backward equation for for diffusion processes      214Ч216
Backward equation for for Kac functional      222Ч224
Backward equation for for Markov chain      143Ч144
Ballot problem      107 134Ч136
Bessel process      175Ч176 327 336
Bessel process, boundary behavior      238Ч239
Bessel process, spectral representation      338
Birth and death process      142
Boundary behavior, and infinitesimal operator      305Ч307
Boundary classifications      234 250
Boundary criteria      232Ч234
Branching process      383 384
Brownian bridge      268 269
Brownian motion      169Ч170 211 323 377 379 385 386 388 389 394
Brownian motion, absorbed      170 392
Brownian motion, and white noise      343
Brownian motion, arcsine law      224Ч226
Brownian motion, backward equation      217
Brownian motion, boundary behavior      228Ч229 230 236
Brownian motion, compounded      378
Brownian motion, conditioned process      267Ч272 388
Brownian motion, control problem      212
Brownian motion, geometric      175 359Ч360 380
Brownian motion, infinitesimal operator      289 297
Brownian motion, instantaneous return process      261
Brownian motion, n-dimensional      291Ч292 299 312Ч313 380 382 393
Brownian motion, radial process      335Ч336
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      513Ч519
Cash inventory model      211Ч212
Chapman Ч Kolmogorov equation      286
Compound Poisson process      426Ч440
Compound Poisson process, decomposition of      433Ч436
Compound Poisson process, sum of      430Ч431
Conditional diffusion process      261Ч272 387
Conditional diffusion process, boundary behavior      263Ч264
Conditional diffusion process, Green function      264Ч265
Conservative diffusion      161
Conservative process      143
Convergence to diffusions      168
Coupling      93
Differential operator      388
Diffusion coefficient      159
Drift coefficient      159
Dynamical systems      343Ч345
Dynkin condition      163 165
Dynkin formula      297Ч299 308Ч313
Dynkin formula, applications      299
Ehrenfest urn model      171
Elastic boundary      255Ч257
Empirical distribution      113Ч116 119Ч123
Entrance boundary      235 246 382
Entrance boundary, stationary distribution      241Ч242
Excessive function      see УSuperregular sequenceФ
Exchangeable random variables      454 516
Exit boundary      233Ч234 246
Exit time      302Ч303
Feller property      291
Forward equation for diffusion processes      219
Forward equation for Markov chain      143 144
Fundamental matrix      24
Gene frequency model      177 206Ч208 361Ч362 381 387 390
Gene frequency model, boundary behavior      239Ч241
Gene frequency model, spectral representation      336Ч337
Gene frequency model, with mutation      177Ч179 180Ч183 208Ч211 239Ч241 265Ч266
Gene frequency model, with mutation and selection      222
Gene frequency model, with selection      180 184Ч188
Genetic recombination      272Ч284
Green function      198Ч202 287
Green function, and resolvent operator      293
Green function, for Brownian motion      205
Harmonic function      see УRegular sequenceФ
Hewitt Ч Savage 0Ч1 law      477
Hille Ч Yosida theorem      296
Hitting time      158 162 192 226
Hitting time of boundary      228 242Ч243
Infinitesimal generator      286
Infinitesimal matrix      145
Infinitesimal mean      159
Infinitesimal operator      195 287 294Ч295
Infinitesimal operator, and boundary behavior      305Ч307
Infinitesimal operator, as differential operator      303Ч305
Infinitesimal operator, domain of      307Ч308
Infinitesimal operator, Dynkin form      300Ч302
Infinitesimal parameters      159
Infinitesimal variance      159
Input distribution      489
Instantaneous return process      260Ч261
Instantaneous state      147
Interchangeable      108Ч113
Ito integral      346Ч347 356Ч357
Ito transformation formula      173 347Ч348 371Ч372 389
Ito transformation formula, applications      374Ч375
Jacobi diffusion      335
Jump boundary      258Ч260
Kac functional      222Ч224 313Ч316 393
Killing rate      204 313Ч316
Killing time      161 382
Killing time, example      272Ч284
Kolmogorov condition      465
Ladder index      95
Ladder random variable      464Ч465 480
Levy process      319 432Ч433
Lightning model      446
Local time      198 207 251Ч253 316Ч324
Local time, inverse of      317Ч318
Logistic equation      360Ч361
Markov time      149Ч150
Martingale      167 308Ч312 325Ч327 371 376Ч377 382
Martingale and stochastic integrals      352Ч355
Maximum random variable      451 463 483Ч484 486
Minimal process      148
Multiplicative functional      313Ч316
Mutation      see also УGene frequency modelФ
Mutation in population      188Ч191
Natural boundary      235Ч236 246
Natural scale      196
Occupation time      252 452
Optimal allocation model      367Ч368
Optimal growth model      366Ч367
Optimal stopping      50Ч64 68Ч69
Option price model      365Ч366 389
Order statistics      100Ч107 124 125 129
Ornstein Ч Uhlenbeck process      170Ч173 183 345Ч346 379 380
Ornstein Ч Uhlenbeck process, backward equation      218
Ornstein Ч Uhlenbeck process, boundary behavior      237
Ornstein Ч Uhlenbeck process, in n dimensions      292
Ornstein Ч Uhlenbeck process, radial process      333Ч334
Ornstein Ч Uhlenbeck process, spectral representation      332Ч333
Ornstein Ч Uhlenbeck process, stationary distribution      221
Periodic class      6Ч10 78
Poisson point process      see also УPoisson processФ
Poisson point process, spatial      436Ч440
Poisson process and uniform distribution      403 404
Poisson process in astronomy      404Ч405
Poisson process, spatial      398Ч403 441 443 445
Population growth model      188Ч191 354Ч355 358 378 382 383 390
Population growth model, boundary behavior      239
Population growth model, geometric      413Ч416
Population growth model, in space and time      416Ч419
Population growth model, spectral representation      334
Population growth model, two types      444
Population growth model, with age structure      419Ч426
Population growth model, with immigration      405Ч408
Population growth model, with mutation      408Ч413
Production and consumption model      363Ч365
Progressively measurable      369
Quasi-left continuity      163
Queue discipline      489
Queueing process      394
Queueing process, $E_k/M/1$      506Ч510
Queueing process, $G/M/^{\infty}$      522
Queueing process, $M/G/^{\infty}$      449 521 522
Queueing process, $M/M/^{\infty}$      519Ч520
Queueing process, embedded Markov chain      497Ч503
Queueing process, G/M/1      504Ч506
Queueing process, GI/G/1      524
Queueing process, GI/GI/1      492Ч496
Queueing process, GI/M/s      511Ч513
Queueing process, M/G/1      523
Queueing process, M/GI/1      497Ч503
Queueing process, M/M/l      490Ч492 519 520 524
Queueing process, M/M/s      519
Queueing process, notation      490
Queueing process, with balking      520Ч521
Quiz show      56Ч58
Radial Brownian motion      see УBessel processФ
Random time change      253Ч255
Random walk      25 26 67 82 97 98 99
Random walk, optimal stopping      58Ч59
Random walk, spectral representation for      10Ч23
Recurrence      72Ч76 83 153 155
Recurrence, criterion for      73
Recurrent class      9 23 35
Recurrent Markov chain      3Ч4 65 66
Recurrent Markov chain, criterion for      37Ч40 47 49
Recurrent state      34
Reflecting barrier      14Ч16
Reflecting boundary      251
Regular boundary      232Ч233
Regular diffusion      158
Regular sequence      44Ч45 83
Renewal Theorem      93Ч95
Renewal theory      482
Resolvent operator      287 292Ч294
Reversed process      42 69
Scale function      194 226
Scale measure      227
Semigroup theory      305
Semigroup theory for Markov processes      285Ч294
Service distribution      489
Shock model      429Ч430
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      1Ч3
Spectral representation, Ornstein Ч Uhlenbeck process      332Ч333
Spectral representation, population growth model      334
Spectral representation, random walk      14Ч18
Speed density      195 197
Speed measure      195 227
SpitzerТs identity      460 472
Stable state      146
Standard process      162
Standard transition function      138
Stationary distribution      220Ч221 236 241Ч242 386
Stationary distribution, generalized      37 42Ч43
Sticky boundary      257Ч258
Stochastic differential equation, solution of      373Ч374
Stopping rule problems      see УOptimal stoppingФ
Stratonovich integral      346Ч347 351 353Ч354 356Ч358 390Ч391
Strength model      439Ч440
Strong Markov property      149Ч152
Subadditive function      139
Subregular sequence      44Ч45
Superregular functions, transient Markov chains      47
Superregular majorant      56 59Ч62
Superregular sequence      44Ч45 52Ч53 66
Taboo probabilities      31Ч32
Total positivity      167
Transience      75
Transient class      24
Transient Markov chain      67
Trap state      378
Unattainable boundary      230
Virtual waiting time      513Ч519
Warrant price model      see УOption price modelФ
White noise      342Ч343
Wong Ч Zakai integral      348Ч351
Wright Ч Fisher model      see УGene frequency modelФ
wronskian      200
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