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Bharucha-Reid A.T. — Elements of the Theory of Markov Processes and Their Applications
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 Applications

Автор: 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.
The book is divided into three parts: Part I, Theory; Part II, Applications; and Appendixes. Part I consists of three chapters which are respectively devoted to processes discrete in space and time, processes discrete in space and continuous in time, and processes continuous in space and time (diffusion processes). In the first two chapters we restrict our attention to Markov chains with a denumerable number of states, with particular reference to branching stochastic processes. The reader interested in chains with a finite number of states should consult, for example, the books of Doob, Feller, Frechet, Kemeny and Snell, and Romonovskii..." A.T.Bharucha-Reid


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 491

Добавлена в каталог: 04.12.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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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