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Àâòîðèçàöèÿ |
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Ïîèñê ïî óêàçàòåëÿì |
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Athreya K.B., Ney P.E. — Branching Processes |
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Ïðåäìåòíûé óêàçàòåëü |
Absolute continuity of W 34 52 172 228
Additive property 3 102 184 201 257
Age distribution, stationary 179
Age-dependent branching process 108 137—180 230—238 248—249
Age-dependent branching process, relation to Galton — Watson process 141—144
Ahlfors, L.V. 53
assumptions 3 12 24 40 58 82 105 118 119 132 139 184 185 192 201
Athreya, K.B. 30 34 55 63 80 85 86 99 118 120 153 172 177 193 206 207 209 220 223 224 234 235 249 250—256 267
Backward equation see Kolmogorov equations
Barucha-Reid, A.T. 239
Basic lemma, critical case 19 113 158 189
Baum, L.F. 160
Bellman, R. 137 147 152n 171 238
Biihler, W.J. 242
Billingsley, P. 211
Binary fission 109 127 239
Birth and death process 109
Blackwell, D. 219
Branching Brownian motion 242—246
Branching diffusions 242—246
Branching random walk 230—238 247—248
Brown, B.J. 56
Brownian motion 242- 246
Cascades 239—242
Chapman — Kolmogorov equation 2 107 257
Chistyakov, V.P. 80 147 148 149 152n 168 171 177
Chover, J. 147 148 152n 159 168 178 226
Chung, K.L. 56 104 119n
Church, J.D. 266 267
Coddington, E.A. 203
Comparison lemma 22
Compound Poisson process 45 126
Conner, H.E. 115 242
Continuous branching function 257—262
Continuous state branching process 257—262 267
Continuous time, Markov branching process 79 102 219
Continuous time, Markov branching process, relation to Gallon — Watson process 110—111 130—135
criticality 8 203 226 256
Darling, D.A. 34 65
Decomposition of processes 47—53 123 143
Density of W 34 37 80 84—87 112 130—131 192
Diffusion 62 242—246 260 261
Directly Riemann integrable 146
Dmitriev, N. 102
Doney, R.A. 180
Doob, J.L. 9 10 121
Dubuc, S. 37 80 93 97 131
Dynkin, E.B. 258
Embeddability problem 130—135
Embedded Galton — Watson process 110—111 130—135 178
Embedded generation process 141—144 228
Embedded urn scheme 219—224
Emigration 266
Environmental process 251
Esty, W.W. Vlll
Exponential limit law see limit law exponential
Extinction time 16 63
Extinction, probability of, age-dependent process 143—144 159 226—227
Extinction, probability of, continuous process 205
Extinction, probability of, continuous time Markov process 107—108
Extinction, probability of, Galton — Watson process 7—8 19
Extinction, probability of, multitype Galton-Watson process 186 188 191
Extinction, process in random environments 252—255
Extinction, transformation to q=0 47—53
Family trees 3 105 137
Feller, W. 35 89 104 145 170 177 180 219
Fisher, R.A. 162
Forward equation see Kolmogorov equations
Foster, J.A. 263 264 265
Freedman, D.A. 221 224
Friedman's urn scheme see Urn schemes
Frobenius theorem 185
Functional equations 10 12 16 29 33 40 43 46 68 112 115 130 172 192 251 258.
Galton — Watson process 1—101 141—144 205 242—246 250 262
Galton — Watson process, relation to age-dependent process 141—144
Galton — Watson process, relation to continuous state branching process 262
Galton — Watson process, relation to continuous time Markov process 110—111 130—135
Galton, Francis 1 2
General time branching process see Age-dependent branching process
Generating function 2 3 4—7 8 67 106—107 115—118 137—139 182—183 200—201 231
Generating function, elementary properties 4—6
Generating function, for age-dependent process 137—139
Generating function, for continuous time Markov process 106—107
Generating function, for multitype process 182 183 200—201 255
Generating function, for stationary measure 68—69 72
Generating function, infinitesimal 106 200—201
Generating function, linear fractional 6—7 22 71—72 109 132—134
Generations 54 141—144 241—242
Gnedenko, B.V. 33
Goldstein, M. 1 141 158 169 226
Green function 66 90—93 98
Green function, truncated 94
Harmonic function 66 93 99 100
Harris, T.E. 2 3 6 7 8 9 34 47 59n 64 67 72 74 99 102 105 107 108 111 116 130 131 132 137 139 147 152n 162 171 172 178 179 181 185 186 193 201 238 239 246 249 251
Heathcote, C.R. 263 264 267
Heyde, C.C. 30 55 56
Imai, H. 80
Immigration 10 262—266 267
Infinite line of descent 49
Infinitesimal generating function 106 200—201
Infinitesimal probability 103—104 201
Instability 8 255 266—267
Integral equations 138 145—146 151—152 179 180 225 226 231 232 237 240
Invariance principle 56
Invariant function see Harmonic function
Invariant measure see Stationary measure
Iteration, functional 2 107 110 138 249 258
Jagers, P. 172
Janossy G-equation 240
Jirina, M. 181 186 257
| Joffe, A. 15 38n 45 186—191 227
Kaplan, N. 256
Karlin, S. 38 n 41 42 68 79 88 99 116 118 120 130—135 185 194 207 224 249 250—256 267
Katz, M. 160
Kemeney, J.G. 66 70 93 98
Kendall, D.G. 2 64 125 127 129 130 136 219
Kesten, H. 20 24 68 73 74 87 88 90—93 94 148 193 209 211 227
Kharlamov, B.P. 242
Kingman, J.F.C. 73 113 115
Knapp, A.W. 66 70 93 98
Kolmogorov equations 103 106 139 200—201 260
Kolmogorov's rock-crushing problem 241
Kolmogorov, A. 3 15 19 33 102 105 113 241 256
Kuczma, M. 131
Kurtz, T. 193
Lamperti, J. 56 58 61 62 125 126 178 257—262
Law of the iterated logarithm 56 129
Levinson, N. 24 139 172 203
Levy, P. 207
Limit law, exponential 20 73 113 169 191 227 256
Limit law, for case 34 65
Limit law, for critical case 18 19—20 61—62 73 113 169 180 191—192 227 256 265
Limit law, for subcritical case 16 18 45 63 64—65 114 170 171 178 186—188 226 227 256
Limit law, for supercritical case 9 16 24 30 33—34 63 80—81 85 86 99 100 112 123—124 136 172 177 179 192 228 256
Limit law, global 80 85 100
Limit law, local 73—82 98 99 100
Linear fractional generating function 6—7 22 71—72 109 132—134
Lipow, C.W. 89
Lipschitz continuity of density 84
Loeve, M.M. 216
Malthusian case 162—167 170 178 226 232—233
Malthusian parameter 146 177 225
Malthusian population growth 9 111 162
Markov branching process see Continuous time Markov branching process
Martin boundary 69 219
Martingale 9 31 111 119 193—194 207 209
Martingale, methods 246—249
McGregor, J. 38n 41 42 68 79 88 116 130—135 207 224 267
Mean see Moments
Mean matrix 184 202 222 225
Minimal process 104 119 201
Mode, C.J. 181 226
Moments, for age-dependent process 143—144 150—158
Moments, for branching random walk 232—238
Moments, for continuous state branching process 259—260
Moments, for continuous time Markov process 108—109 111
Moments, for Galton — Watson process 4
Moments, for multitype branching process 184—185
Moments, for multitype continuous time Markov process 202—205
Monotone ratio lemma 12
Mullikin, T.W. 181 189 191
Multitype branching process 181—228 265
Multitype, age-dependent 225—227 228
Multitype, continuous time Markov 199 209
Neuts, M.F. 64
Neveu, J. 66
Ney, P. 20 58 61 62 68 73 74 80 85 86 87 88 90—93 94 99 147 148 152n 159 168 178 189 192 226 230 232 233 234 235 236 240
Non-explosion hypothesis 104 177 201 222 228 261
Non-singular process 184
Nucleon cascades 239—242
Pakes, A.G. 267
Papangelou, F. 11 15
Pinsky, M.A. 267
Poisson process 125 130 263
Polya's urn scheme see Urn schemes
Positive regular 184 202
Potential theory 66—101
Q-process 56—60 62 64
Queueing process, relation to branching process 64
Random environments 249—256 267
Ratio theorem 15
Renewal function 66 144 see
Renewal theory 144—150 232 237
Reproductive age value 249
Ryan, T.A., Jr. 163 170 226
Samuels, M.L. 235 242
Savits,T.H. 105 139 201 256
Selivanov, B. 1 38n
Seneta, E. 11 15 18 24 30 33 34 38n 41 65 179 228 257 264 265 267
Sevastyanov, B.A. 102 116 159 263
Sims, J. 94
Slack, R.S. 19 20 100
Slowly varying 63
Smith, W.L. 249—250 252 254
Snell, J.L. 66 70 93 98
Snow, R.N. 226
Space time boundary 98—99
Spectral representation 41—42 79 178 267
Spitzer, F. 20 22 38n 45 58 61 66 68 69 73 74 87 88 90—93 94 186—187 189—191 227 232
Split times 118—123 154 206—209 221
Stationary age distribution 179
Stationary distribution 66
Stationary measure 66 73 87—89 91 100
Stigum, B.P. 24 34 193 209 211 227
Sub-exponential case 168—169 171 235—236
Sub-exponential class 147—150
Total number of particles 180
Transience 7—8 186 266—267
Type-space 246 249
Urn schemes 219—224 228
Vere-Jones, D. 15 257
Vinogradov, O.P. 147 163
Wainger, S. 147 148 152 168 178
Watanabe, S. 125 242 245 246 257
Watson, H.W. 2
Weiner, H.J. 226 227
Wilkinson, W.E. 249—250 252 254
Williamson, J.A. 64 264 265
Yaglom theorem 18 114 170 186—187 256
Yaglom, A.M. 15 20 113
Yule process 109 127—130 136
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