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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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Absolute probability 13 Absorbing barrier process 145—147 Absorption probabilities 17 18 52 152 153 Ackoff, R.L. 434 456 Agarwal, S. 213 Age distribution of populations 188 Age-dependent branching processes see "Bellman — Harris process" "Waugh Agekyan, T.A. 346 357 Albert, G.E. 308 331 Approximating systems for stochastic epidemics 209 210 Arley, N. 5 118 124 231 248 289 Armitage, P. 124 193 196 230 Arnoff, E.L. 434 456 Arrival times 375 Arrow, K. 434 Ashcroft, H. 404 414 416 434 Austin, D.G. 124 Backward Kolmogorov diffusion equation 132 Bailey, N.T.J. 85n. 124 199 201—203 207 212 230 382 383n. 425 434 Balking distribution 429 Bartholomay, A.F. 230 360—362 372 455 456 Bartlett — McKendrick epidemic process 204—208 Bartlett — McKendrick epidemic process in cascade theory 288 Bartlett — McKendrick epidemic process in epidemic theory 211 212 Bartlett — McKendrick epidemic process in mutation theory 196—198 Bartlett — McKendrick epidemic process in nuclear emulsion research 318 Bartlett — McKendrick epidemic process in population growth 186—189 Bartlett — McKendrick epidemic process, limit theorems for 115—117 Bartlett — McKendrick epidemic process, moments of 96—97 Bartlett, M.S. 5 41 53 198 199 211 230 264 289 434 452 455 456 Bass, L. 289 Bateman, H. 296 331 Bay, Z. 331 Beach, L.A. 455 Bekessy, A. 331 Belenkif, S.Z. 289 294 Bellman, E. 38n. 53 65 67n. 70 95 97 98 100 111 118 124 187 188 303n. 331 Benes, V.E. 393 434 Benson, F. 411n. 434 Berger, M.J. 455 Bernstein, I.B. 289 Bethe, H. 239n. 289 Bhabha, H.J. 236 238 246 247 249 256 289 Bharucha-Reid, A.T. 52n. 53 100n. 123n. 124n. 125 128 211n. 230 289 294 372 Birth process 77—82 Birth process from Bellman — Harris process 98 99 Birth process in chemistry 360 361 Birth process in population migration 185—186 Birth process, deterministic 2 170 Birth process, diffusion equation representation of 190—192 Birth process, dishonest 81 Birth process, linear 77—80 Birth process, non-Markovian 99 Birth process, nonhomogeneous see "Polya process" Birth process, nonlinear 77n. Birth process, simple 77—80 Birth, death, and immigration process 173—174 Birth-and-death process 86—94 Birth-and-death process from Bellman — Harris process 99 Birth-and-death process from Waugh process 100 189 Birth-and-death process in queueing theory 383—385 Birth-and-death process limit theorems 103 104 108—111 Birth-and-death process uniqueness problem 91—93 Birth-and-death process, artificial realization of 450—452 Birth-and-death process, bivariate 176—179 182—184 204—209 Birth-and-death process, classification of 93 94 Birth-and-death process, cumulative 171—173 Birth-and-death process, distribution of maximum of sample function 104 Birth-and-death process, logistic 122 175 Birth-and-death process, nonhomogeneous 89—91 169—173 Birth-and-death process, quadratic 87n. Blackwell, D. 28n. 53 309 331 Blanc-Lapierre, A. 5 130 Blatt, J.M. 317 323 331 Bochner, S. 5 130 162 264 289 Borchsenius, V. 124 Boundaries, classification of 143—145 160 Boundary entrance 144 Boundary exit 143 Boundary, absorbing 139 Boundary, accessible 143 Boundary, inaccessible 143 Boundary, natural 143 144 Boundary, reflecting 139 Boundary, regular 143 Bourbaki, N. 65 125 Branching process of a special form 111—115 Branching processes and random walk 44—47 Breiman, L. 92 125 Brockmeyer, E. 374n. 434 Brownian motion 139 140 Busbridge, I.W. 351 357 Butcher, J.C. 289 290 455 456 Camp, G.D. 456 Carlson, J.F. 236 290 Carslaw, H.S. 447 Castoldi, L. 26 53 Cerkasov, I.D. 161 162 Chadwick, J. 296 332 Chakrabarty, S.K. 238 246 289 Champernowne, D.G. 382 434 Chandrasekar, S. 334—336 339 351 355 357 Chapman — Kolmogorov functional equation 13 59 61 63 118 130 Characteristic functional 264 265 277—282 Chartres, B.A. 287 290 Chemical reactions chain 366—371 Chemical reactions, autocatalytic 360 361 Chemical reactions, bimolecular 362 Chemical reactions, diffusion-controlled 371 372 Chemical reactions, monomolecular 365 366 Chemical reactions, unimolecular 361 362 Chiang, C.L. 181 184 231 Chung, K.L. 5 28 30 31 53 62n. 125 Churchill, R.V. 447 Churchman, C.W. 434 449 456 Cistyakov, V.P. 118 125 Clarke, A.B. 382 434 Classification of boundaries 143—145 160 Clementel, E. 290 Closed class 50 Closed set of states 14 Coefficients of variation 123 248 Coefficients, of loss 413 Cohen, J.W. 404n. 435 Communicating states 14 Competitive and predatory populations 179—184 Compound distribution 96 441 Conditional probability 4 5 11 Conditional probability, constant 11 Conditional probability, limiting behavior 37—39 Conditional probability, stationary 11 Consael, R. 89n. 127 232 Continuant 93 Continuous parameter martingale 124 Contraction mappings, principle of 52 Convolution 10 441 Coppinger, J. 436 Coulson, C.A. 193 232 Cox, D.R. 411n. 414 434 435 Cramer, H. 22n. 53 Critical point of a Markov process 105 Crone, I.W. 449 456 Crow, J.F. 215 213 Cumulant generating function 21 172 Cumulants 21 Cumulative population size 42 Cumulative process 171—173 Czerwonko, J. 263 290 D'Ancona, U. 180 231 Darkening, law of 354—357 Darling, D.A. 148 162 Darwin, J.H. 231 Davis, G. 232 332 Death process 85—86 Death process in chemistry 362 Death process in epidemic theory 199—203 Death process, deterministic 170 Death process, linear 85 86 Death process, nonlinear 85n. 199—203 Death process, simple 85 86 Decomposable chain 14 Degenerate branching process 49 Delbrueck, M. 193 233 360 372 Density field, fluctuating 339—346 Dependent 5 Derman's theorem 30 31 Derman, C. 30 31 53 Diffusion processes in genetics 213—222 Diffusion processes in nuclear reactor theory 331 Diffusion processes in population growth 189—192 Diffusion processes, and branching processes 154—156 Diffusion processes, first-passage time problems 148—152 Diffusion processes, maximum distribution of 153 154 Diffusion processes, transformations of 161 Discrete branching process 10 Discrete parameter martingale 40 Discrete process, diffusion equation representation of 154—158 Dishonest processes 71n. 81 92 Dissipative chain 34 Dmitriev, N.A. 55 Dobrushin, R.L. 92 125 Doeblin, W 41 53 Doetsch, G. 447 Doig, A. 435 Doob, J.L. vii 3—5 40 63n. 72 103 124n. 125 130 309 331 Downton, F. 425 429 435 Dynkin, E.B. 5 Edlund, M.C. 324 331 Ehrenfest process 122 Electron-photon cascade 235 Electron-photon cascade, fluctuation problem for 246—265 Elementary return process 145 Ellis, C.D. 296 332 Emission, probability distribution of 353 354 Epidemic curve 203 Epidemics, small groups 212 213 Epidemics, two populations 208 209 Equilibrium distribution 28 Erdelyi, A. 448 Ergodic theorems 28—37 102—104 Erlang's loss formula 406 Erlang, A.K. 374 376 397 Everett, C.J. 48 51 53 Extinction, number of generations to 26 27 Extinction, probability of 18 47 89—91 98 170 171 179 191 see "Gambler's Fagen, R.E. 437 Fay, H. 290 Feller integrodifferential equations 60 120 Feller — Lundberg theorem 81 82 91 Feller, W. vii 5 28n. 31n. 52n. 53 54 60 64 72 97 125 129 130 136 142—145 148 154n. 162 168 175 190 215 231 300 303n. 331 409 412 438 442 Fermi, E. 330 Feshbach, H. 216 233 Final class 50 First-passage time 17 93 148 First-passage time problems for diffusion processes 148—154 First-passage time problems in genetics 222 First-passage time problems, in chemistry 371 Fisher, R.A. 39 54 231 Fission detectors 313—316 Fisz, M. 5 77 125 Fixed points 24 52 Florek, K. 77 125 Fluctuating density field 339—346 Fluctuation problems, electron-photon cascades 246—265 Fluctuation problems, nucleon cascades 270—276 Fluctuation, relative (coefficient of variation) 123 248 Fokker — Planck equation 133 145—147 213—222 331 Fomin, S.V. 52n. 55 Forsythe, G.E. 456 Fortet, R. 5 54 130 162 192n. 231 435 Forward Kolmogorov diffusion equation 133 Foster, F.G. 17 34 35 54 207 231 378 381 435 455 456 Frechet, M. vii 5 Fry, T.C. 416 435 Functional iterates 19 24 Fundamental theorem for branching processes 24 52 381 Furry, W.H. 247 290 Gaffey, W.R. 213 231 Galaxies, model of simple clustering 347—350 Galton — Watson process 98 99 Galton, F.S. 23 24n. 54 Gambler's ruin problem 46—47 53n. Ganguly, S. 290 Gani, J. 435 Gardiner, V. 452 456 Gardner, J.W. 288—290 Gellman, H. 290 Gene fixation, ultimate probability of 222 Gene frequency, maximum, distribution of 222 223 General counter model 307 Generalized classical boundary conditions 146 Generalized discrete branching process 36 Generalized discrete branching process, limit theorems for 35—37 Generating functions 18 439 Generating functions and moments 20—23 Generating functions and sums of independent random variables 441 Generating functions and transition probabilities 18—19 Generating functions, Maclaurin's expansion of 441—442 Generating functions, partial fraction resolution of 442 Germond, H.H. 456 Girault, M. 435 Glasstone, S. 324 331 Gnedenko, B.V. 5 22n. 27 54 331 Goldberg, S. viii 215 216 231 Good, I.J. 45 54 Goodman, L.A. 176 179 231 Green, H.S. 287 292 Greenwood, M. 212 Greisen, K. 239n. 293 Gupta, M.R. 290 Gurk, H.M. 395 435 H-equation 364—367 Hadamard, J. 24 54 Haight, F.A. 425 435 Hall, W.J. 125 Halmos, P.R. 6 69n. 126 Halstrom, H.L. 374n. 434 Hammerstey, J.M. 332 449 456 Happ, W.W. 322 332 Harris, T.E. 6 26 40n. 41 45 48 50 52n. 54 95 97 98 100 111 118 124 126 187 188 231 257n. 290 Haskey, H.W. 203 208 209 231 Hawkins, D. 25n. 42n. 54 Heat equation 139 Heitler, W. 236 239n. 247 257n. 266 289 290 Hellinger, E. 93 126 Herz, A.J. 323 332 Hille, E. 6 13n. 54 64n. 72 121n. 126 136 143 162 Hoffman, J.G. 452 456 Homma, T. 381 406 435 Householder, A.S. 449 455n. 456 Hull, T.E. 322 332 Imbedded Markov chain 377—381 426—429 Indecomposable chain 14 Independent increments, process with 121 Infinitesimal transition probabilities 63 Instantaneous return process 145—147 Integral equation, Chandrasekar — Muench 336—339 346 Integral equation, renewal type 97 302 303 Integral equation, Wiener — Hopf 395 Intensity function 59 62 105 119 157
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