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Bailey N.T.J. — The Elements of Stochastic Processes With Applications to the Natural Sciences.
Bailey N.T.J. — The Elements of Stochastic Processes With Applications to the Natural Sciences.



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Название: The Elements of Stochastic Processes With Applications to the Natural Sciences.

Автор: Bailey N.T.J.

Аннотация:

Develops an introductory and relatively simple account of the theory and application of the evolutionary type of stochastic process. Professor Bailey adopts the heuristic approach of applied mathematics and develops both theoretical principles and applied techniques simultaneously.


Язык: en

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 130

Добавлена в каталог: 21.05.2005

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