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Bharucha-Reid A.T. — Elements of the Theory of Markov Processes and Their Applications
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Название: Elements of the Theory of Markov Processes and Their ApplicationsАвтор: Bharucha-Reid A.T. Аннотация: "My purpose in this book is twofold: first, to present a nonmeasure-theoretic introduction to Markov processes, and second, to give a formal treatment of mathematical models based on this theory which have been employed in various fields. Since the main emphasis is on applications, this book is intended as a text and reference in applied probability theory.
Язык: Рубрика: Математика /Серия: Сделано в холле Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 491Добавлена в каталог: 04.12.2010Операции: Положить на полку |
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Interarrival times 375 Interference loss 412 Inverse probabilities 31 Ionescu Tulcea, C.T. 6 Ionization cascade 276 Irreducible chain 14 Ito, K. 6 130 162 Ivanenko, I.P. 290 Iversen, S. 231 Jackson, R.R.P. 435 Jacobi matrix 44n. Jaeger, J.C. 447 Janossy functions 276 Janossy G-equations 256—264 273—276 Janossy, L. 256 257n. 261n. 266 276 288 290 291 332 Jensen, A. 71n. 126 374n. 434 Jirina, M. 51 54 118 126 John, P.W.M. 77n. 87n. 91n. 92 122n. 126 Jordan, Ch. 251n. Joshi, D.D. 176 179 231 Kac, M. 44n. 54 162 Kahn, H. 449 456 Kakutani, S. 32 56 Kalaba, R. 53 Kamata, K. 287 291 Kantorovic, L. 52 54 Kapadia, P.D. 288 Karlin, S. 44n. 54 55 87n. 92—94 103 126 382 434 435 Kato, T. 72 126 Kawada, Y. 6 Kawata, T. 381 425 435 Kemeny, J.G. vii 6 Kempthorne, O. 215 231 Kendall, D.G. 35 55 72 89 99 100 103 126 127 171 172 175 176 187 189 198 205 209 210 232 264 289 376 377 381 391 403 435 450 455 457 Kermack — McKendrick equations 205 Kermack — McKendrick equations, threshold theorem for 205—208 Kermack, W.O. 205 Kesten, H. 436 Khintchine, A. 6 130 162 416 436 Khristov, Kh.Ia. 291 Kiefer, J. 436 Kim, S.K. 371 372 Kimura, M. 215 216 219 222 231 232 King, G.W. 372 455 Klahr, C.N. 331 332 Koenig's Theorem 38 Koenigs, G. 38 55 Koenigsberg, E. 436 Kolmogorov differential equations 61 120 Kolmogorov differential equations for birth process 79—80 Kolmogorov differential equations for birth-and-death process 90—91 Kolmogorov differential equations for death process 86 Kolmogorov differential equations for Polya process 84 85 Kolmogorov differential equations, existence and uniqueness theory of 64—72 Kolmogorov differential equations, matrix form 63 Kolmogorov diffusion equations 130—139 160 Kolmogorov diffusion equations in genetics 213—223 Kolmogorov diffusion equations, existence and uniqueness theory of 136 144 145 Kolmogorov diffusion equations, methods of solving 136—139 Kolmogorov, A.N. 6 11 22n. 27 32 48 52n. 54 55 61 127 129 154n. 162 214 232 397 436 Konwent, H. 262 263 291 Koopman, B.O. 92 93 127 Kosten, L. 332 Kostitzin, V.A. 180 232 Kourganoff, V. 351 357 Kronig, R. 436 Kunisawa, K. 6 Kunz, K.S. 428n. 436 Kuratowski, C. 106n. Kurbatov, J.D. 332 Laidler, K.J. 372 Lamb, W.E. 248 292 Lamens, A. 89n. 127 176n. 232 Landau — Rumer equations 239—246 Landau, H.G. 230 Landau, L. 238 291 Laplace transform 443—447 Laplace transform inversion theorem 444 Laplace — Stieltjes transform 444 Lateral condition 145n. Lattice distribution 309 Law of mass action 364 Lea, D.E. 193 223 232 Ledermann, W. 64 91 121 127 382 385n. 436 Leslie, P.H. 233 452 457 Lethargy of neutron 324—330 Levert, C. 332 Levy, P. 6 62n. 102 127 130 Limit point of a Markov process 105 Limit sets of sample functions 105—108 Lindley, D.V. 393 395 436 Litwiniszyn, J. 130 162 Loeve, M. 6 156 Logistic process 122 175 192 Lopuszanski, J. viii 260—263 273 274 291 Loss formula, Erlang's 406 Lost call, probability of 403—406 Lost calls, expected number 406 Lotka, A.J. 180 233 Luchak, G. 382 436 Lundberg, O. 6 Luria, S.E. 193 233 Machine availability 413 Machine efficiency 413 Machine interference models, Palm's 408—414 Machine interference models, Takac's 414—419 Machines in repair, average number 412 Machines in working condition, average number 412 Machines repairman, patrolling 419—425 Machines repairmen, average number idle 412 Machines repairmen, expectation of busy time 418 Machines waiting line, average number in 412 Machines waiting time, distribution function of 418 Machines waiting time, expectation of 418 Machines, production times 417 Malecot, G. 215 233 442 Mann, H.B. 6 332 Marchand, H. 233 Marczewski, E. viii 77 105n. 125 127 Markov chain 4 10 11 Markov chain classification of states 13—17 Markov chain with continuous time parameter 61 Markov chain, dissipative 34 Markov chain, ergodic 378 Markov chain, nondissipative 34 Markov chain, periodic 52 Markov chain, recurrent 379 Markov chain, semidissipative 34 Markov chain, stationary 62 Markov chain, time-homogeneous 62 Markov chain, transient 62 Markov matrix 12 Markov process 4 58 Markov process diffusion 129 Markov process, discontinuous 57 Markov process, dishonest 71n. 81 92 Markov process, limit point 105 Markov process, mixed 194 387 Markov process, N-dimensional diffusion 158—160 Markov process, N-dimensional discontinuous 118—121 Markov process, periodic 124 Markov process, sample function 63 Markov property 11 Markov, A.A. 4n. Marshall, B.O. 436 Martingale convergence theorem 40 Martingale, continuous parameter 124 Martingale, discrete parameter 40 Maruyama, G. 130 163 Mass action, law of 364 Mathews, P.M. 256 288 289 293 332 336 338n. 358 Matrix of transition probabilities 12 Maximum gene frequency 222 223 McCloskey, J. 436 McGregor, J. 44n. 54 55 87n. 92—94 103 126 382 435 McKean, H.P. 130 162 163 McKendrick, A.G. 199 205 233 McLachlan, N.W. 448 McMillan, B. 393 436 McVittie, G.C. 357 Mean ergodic theorem 32—34 Mean first-passage time 17 Mean recurrence time 17 Medgyessy, P. 372 Mellin transform 443 447 Mellin transform, inversion theorem 447 Messel, H. viii 246n. 248 261 263 267 269 270 275 276n. 287—292 455 456 Metropolis, N. 449 452 456 457 Metzler, W.H. 233 Meyer, H.A. 449 457 Migration probability function 185 Mihoc, G. 6 Milky Way, fluctuations in brightness 335—347 Miller, R.G. 425 437 Mitra, A.N. 248n. 292 Mixed Markov process 194 387 Models 1—3 168 Models, deterministic 1—3 Models, stochastic 1—3 Mogyorodi, J. 331 332 Molina, E.C. 397 410n. 437 Moments, truncated 131 132 Mondria, H. 436 Monte Carlo methods 449 Monte Carlo methods in biology 184 211 212 452 455 Monte Carlo methods in chemistry 455 Monte Carlo methods in operations research 455 456 Monte Carlo methods in physics 246 288 289 455 Montroll, E.W. 371—373 Moorish, A.H. 322 332 Moran, P.A.P. 215 233 Morgenstem, D. 81 127 Morse, P.M. 216 233 382 437 Morton, K.W. 456 Moyal, J.E. 57 127 276 292 Muench, G. 334—336 339 357 Muir, T. 233 Mutation processes, age-dependent theory of 196—198 Mutation processes, effect of phenotypic delay on 198 Mutation processes, single 193 Mycielski, J. 332 N-component cascade processes 287—288 N-dimensional branching processes 47—51 N-dimensional branching processes, fundamental theorem for 49—50 N-dimensional branching processes, limit theorems for 49—51 N-dimensional branching processes, moments of 48 49 N-dimensional Markov process, diffusion 158—160 N-dimensional Markov process, discontinuous 118—121 n-step transition probabilities 12 n-step transition probabilities, limiting behavior 28—37 Nakamura, G. 438 Naor, P. 410 412 413 437 Nelson, L. 308 331 Nemeth, G. 331 332 Neveu, J. 130 148n. 163 Neyman, J. 184 233 334 347 357 Nickols, D.G. 435 Nishimera, J. 287 291 Nondissipative chains 34 Nordsieck, A. 248 292 Normed random variables 39—41 116 Nucleon cascades 237 Nucleon cascades, fluctuation problem for 270—276 O'Ceallaigh, C. 322 323 Olbert, S. 287 292 Olsson, O. 332 Onicescu, O. 6 Opatowski, I. 127 223 233 Operative efficiency 413 Oppenheimer, J.R. 236 290 Ornstein, L.S. 140n. 163 Otter, R. 10n. 42n. 43 55 Pakshirajan, R.P. viii Pal, L. 292 314 331 332 Palm's machine interference models 408—414 Palm, C. 403 408 409 412 414 416 437 Park, T. 184 233 Patil, V.T. 233 Pearl — Verhulst equation 192 Petrovskii, I. 214 232 Phenotypic delay 198 Phillips, R.S. 6 13n. 54 64n. 72 126 162 Picard, E. 24 55 Pinney, E. 73n. 127 Pinsker, A.G. 54 Piscounov, N. 214 232 Poisson distribution 74 186 Poisson process 73—77 Poisson process in cascade theory 247 248 Poisson process in population migration 186 Poisson process in theory of radioactive transformations 298 Poisson process, composed 77 Poisson process, nonhomogeneous 77 Pollaczek, F. 403n. 437 Polya process 82—85 Polya process in cascade theory 248 Polya process relationship to Poisson and Yule — Furry processes 84 Polya process, Kolmogorov equations for 84—85 Polymer chains 372 Popov, Iu.A. 292 Population growth, diffusion equation representation 189—192 Population migration 184—186 Populations, competitive and predatory 179—184 Potts, R.B. 263 269 270 275 288 292 Powell, E.O. 187n. 233 Preisendorfer, R.W. 351 357 Prekopa, A. 77 127 372 373 Prendiville, B.J. 175 Principle of contraction mappings 52 Probability function 58 Probability function, absolute 58 Probability function, conditional 58 Product density functions 249—256 283—287 347 Puppi, G. 290 Pyke, R. 185 332 Quasi-process 71n. Queueing systems discipline 375 Queueing systems input process 375 Queueing systems input process arrival times 375 Queueing systems input process interarrival times 375 Queueing systems representation integral equation 393—395 Queueing systems representation integrodifferential equation 385—393 Queueing systems representation Markov chain 377—381 Queueing systems representation, differential-difference equations 381—385 Queueing systems service mechanism 375 Queueing systems service times 375 376 Queueing systems, description 376 Queues, balking 429—434 Queues, bulk-service 425—429 Queues, ergodic 378 379 Queues, non-Markovian 399—403 414—419 Queues, recurrent 379 Queues, transient 379 see "Machines" "Service "Telephone Radiation damage, birth-and-death model 223—227 Radiation damage, random-walk model 227—230 Radiobiology see "Radiation damage" Ramakrishnan, A. 127 249 256 276 282 283 287—289 292 293 332 334 336 338n. 339 346 347 357 358 Random drift 215—219 Random walk 44 Random walk and branching processes 44—47
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