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| Авторизация |
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| Bailey N.T.J. — The Elements of Stochastic Processes With Applications to the Natural Sciences. |
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| Предметный указатель |
"Random-variable" technique 70
"Rush-hour" theory 157
Absolute probabilities 39
Absorbing barrier 24 176
Accidents 68
Additive process 202
Age-dependent branching process 230
Aperiodic Markov chain 47
Aperiodic state 44
Appointment systems, in hospital outpatient departments 147
Approximations 207 ff.
Approximations, asymptotic, in queueing theory 155 156
Approximations, continuous 207
Approximations, neglect of high-order cumulants 217
Approximations, saddle-point 214
Approximations, steepest descents 214
Approximations, stochastic linearization 219
Arley, N. 114
Armitage, P. 126
Asymptotic approximations 4
Asymptotic approximations in queueing theory 155 156
Augmentation technique 223
Backward equation for diffusion process 200 201
Backward equation for Markov process 78
Bacteria, mutation in 125
Bacterium aerogenes 131
Bailey, N.T.J. 2 137 147 156 162 166—168 175 184 224 226 228
Barriers in random walk, absorbing 24 176
Barriers in random walk, elastic 25
Barriers in random walk, reflecting 25
Bartlett, M.S. 4 88 126 162 186 188 192 193 219 228
Bharucha-Reid, A.T. 4 101 107 119 137 201 204 228
Birth process, diffusion approximation for 210
Birth process, divergent 89
Birth process, explosive 89
Birth process, general 88
Birth process, multiple-phase 131
Birth process, simple 84 232
Birth-and-death process 3 84
Birth-and-death process, effect of immigration in 97 115
Birth-and-death process, general 101
Birth-and-death process, homogeneous 84 ff.
Birth-and-death process, non-homogeneous 110
Birth-and-death process, simple 91 232
Branching process 10
Branching process, age-dependent 230
Branching process, continuous approximation to 207
Branching process, discrete 58 ff.
Brownian motion, of colloidal particles 100 194
Bush, R.R. 51
Chain-binomial models, in epidemic theory 182
Chance of adequate contact, in epidemics 183
Chandrasekhar, S. 100
Chapman — Kolmogorov equations 76
Chapman — Kolmogorov equations for diffusion processes 199
Chapman — Kolmogorov equations for Markov chains 76
Characteristic function 13
Chromosomes, breakage of 66 68
Chromosomes, mapping of 226
Clarke, A.B. 161
Collar, A.R. 3 50
Colloidal particles, motion of 100 194
Competition and predation 186 ff.
Competition between two species 187
Compound distribution 9
conditional probabilities 39
Continuous variables in continuous time 194
Convolution 7
Copson, E.T. 3 12 33 214
Coulson, C.A. 129
Cox, D.R. 21 137 151 223
Cumulant-generating function 7 12
Cumulants, generating function for 7 12
Cumulants, neglect of high order 217
Cumulative population, treatment of 120
Daniels, H.E. 207 214
Darwin, C. 1
Death process, general 91
Death process, simple 90
DeBruijn, N.G. 4 214
Delayed recurrent events 21 45
Deterministic growth 87 89 94
Deterministic model 2
Deterministic model in competition between species 187
Deterministic model in epidemics 164 170 177
Deterministic model in prey-predator relationship 189
Deterministic threshold theorem, in epidemics 172
Differential equations 3
Differential equations for stochastic moments 96
Differential equations, Kolmogorov backward 78
Differential equations, Kolmogorov forward 77
Differential equations, solution of partial 74 202
Differential-difference equations 67
Diffusion coefficient 196
Diffusion equations 197 199—201
Diffusion equations, singular 201
Diffusion equations, solution of 202
Diffusion processes 194 ff.
Diffusion processes as limit of discrete branching processes 197
Diffusion processes as limit of random walk 195
Diffusion processes, additive 202
Diffusion processes, application to population growth 205
Diffusion processes, general theory of 199
Diffusion processes, homogeneous 202
Discrete variables in continuous time 66 ff.
Discrete variables in discrete time 16—65
Divergent birth process 89
Divergent growth 80
Doob, J.L. 3
Drift, in diffusion process, 196
Duncan, W.J. 3 50
Duration of game, in gambler's ruin problem 27
Duration time, of simple stochastic epidemic 168
Eigenfunction 203
Eigenvalue 47 203
Eigenvector 47
Elastic barrier 25
Epidemic processes 2 162
Epidemic processes, chain-binomial models for 182
Epidemic processes, deterministic 164 170 177
Epidemic processes, general 169
Epidemic processes, recurrent 177
Epidemic processes, simple 164
Epidemic processes, stochastic 165 172 179
Erdelyi, A. 153
Ergodic process 80
Ergodic state 44
Event 16
Event, delayed recurrent 21
Event, periodic 18
Event, persistent 18
Event, recurrent 16
Event, transient 18
Evolution 1 87
Evolutionary process 4
Explosive birth process 89
Explosive growth 61 80
Exponential distribution see Negative exponential distribution
Extinction, probability of 60 95
Factorial moment-generating function 7 14
Factorial moments, generating function for 7 14
Family names, survival of 59
Feller, W. 3 5 12 16 18 19 21 22 27 34 38 42 51 90
First-passage time 30
First-passage time in diffusion processes 204
First-passage time in queueing theory 157
Fisher, R.A. 56
Fokker — Planck equation 197 201
Forsyth, A.R. 4 74 209
Forward equation for diffusion process 199—201
| Forward equation for Markov process 77
Foster, F.G. 47
Fourier transform 13
Frazer, R.A. 3 50
Frost, W.H. 183
Furry, W.H. 87
Gambler's ruin 25
Gambler's ruin, expected duration of game 27
Gambler's ruin, probability of ruin at nth trial 28
Gambler's ruin, probability of ruin over-all 25
Gause, G.F. 192 193
General birth process 88
General birth-and-death process 101
General death process 91
General epidemics 169
Generating function 3 5
Generating function, cumulant 7 12
Generating function, factorial moment 7 14
Generating function, moment 7 12
Generating function, probability 6
Genetic linkage 227
Goldberg, S. 26
Greenwood's chain binomial 183
Greenwood, M. 183
Haskey, H.W. 168
Heraclitus 1
Homogeneous birth-and-death process 84 ff.
Homogeneous Markov chain 40
Hospital beds, demand for 143
Hospitals, function and design of 136
Imbedded Markov chain 138 222
Immigration, effect of, on birth-and-death process 97 115
Inbreeding 53
Incubation period 163
Infectious period, in epidemics 163
Input process, of a queue 137
Integral equations, use of 228
Interaction between species 186
Interference, in genetics 227
Irreducible Markov chain 42
Kelly, C.D. 131
Kemeny, J.G. 38
Kendall, D.G. 121 125 131—134
Kermack and McKendrick's Threshold Theorem 172
Kermack, W.O. 172 176
Kolmogorov, backward differential equation 78
Kolmogorov, backward diffusion equation 200 201
Kolmogorov, forward differential equation 77
Kolmogorov, forward diffusion equation 199 201
Lagrange's formula, for the reversion of series 33
Laplace transform 3 142
Laplace transform for solving differential-difference equations 151 166
Laplace transform for solving partial differential equations 203
Latent period, in epidemics 163
Lea, D.E. 129
Lindley, D.V. 229
Linearization, stochastic 219
Lotka, A.J. 186
Map distance, in genetics 227
Markov chain 38 ff.
Markov chain, aperiodic 47
Markov chain, classification of chains 46
Markov chain, classification of states 41
Markov chain, ergodic 46
Markov chain, finite 40 46
Markov chain, homogeneous 40
Markov chain, imbedded 138
Markov chain, irreducible 42
Markov chain, limiting distribution of 46
Markov chain, stationary distribution of 47
Markov process 66 ff.
Markov process, ergodic 80
Markov process, general theory of 75
Markov property 38 66
Matrix, calculating powers of 47
Matrix, spectral resolution of 48
McKendrick, A.G. 172 176
McLachlan, N.W. 3
Metric, in genetics 226
Molina, E.C 146
Moment-generating function 7 12
Moments, generating function for 7 12
Monte Carlo methods in appointment systems 147
Monte Carlo methods in prey-predator model 193
Moran, P.A.P. 201
Mosteller, F. 51
Multidimensional process 117 ff. 222
Multiple-phase birth process 131
Multiplicative process 59 102
Mutants 66
Mutants in bacteria 125
Mutants, branching process for spread of 63
Mutation in bacteria 125
Negative binomial distribution 87 99 109
Negative exponential distribution 68
Newton, Isaac 1
Non-homogeneous process 107 ff.
Non-homogeneous process for birth and death 110
Non-homogeneous process, chance of extinction in 112
Non-homogeneous process, effect of immigration on 115
Non-Markovian processes 222 ff.
Normal approximation to stochastic process 208 218
Nuclear chain reaction 61
Null state 44
Operations research 136
P61ya, G. 34
Paramecium aurelia 192
Park, T. 188
Partial differential equations 69 ff
Partial differential equations, solution of linear 74
Partial differential equations, solution of second-order 202
Partial fractions 10
Partial fractions in expansions of generating functions 10
Parzen, E. 3 4 13
Periodic event 18
Periodic recurrent event 18
Periodic state 44
Persistent event 18
Persistent state 44
Poisson process 67
Poisson process, diffusion approximation for 208
Polya process 107
Population growth with two sexes 119
Population growth, birth-and-death processes for 84 ff.
Population growth, branching processes in 58
Population growth, diffusion processes in 205
Predation 189
Predation, competition and 186 ff.
Prey-predator model 189
probability distribution 2
Probability distribution, absolute 39
Probability distribution, conditional 39
Probability process 2
Probability-generating function 6
Process see under particular kind of process e.g.
Queue discipline 137
Queue length, distribution of 141
Queueing process 2 136
Queueing process with many servers 143
Queueing process, continuous time treatments of 149
Queueing process, equilibrium theory of 137
Queueing process, first-passage time for 157
Queueing process, generalized 229
Queueing process, non-equilibrium treatment of 149
Queues, theory of 136 ff.
Radioactive disintegration 66 67
Rahn, O. 131
Random variable 6
Random walk 24
Random walk in epidemics 176
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