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Kannan D. — An introduction to stochastic processes
Kannan D. — An introduction to stochastic processes

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Название: An introduction to stochastic processes

Автор: Kannan D.

Язык: en

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 296

Добавлена в каталог: 04.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\sigma$-algebra(s)      3
$\sigma$-algebra(s), Borel      4
$\sigma$-algebra(s), generated by a random vector      8
$\sigma$-algebra(s), independent      13
$\sigma$-algebra(s), tail      13
Absorbed process      275
Absorbing barrier      43
Absorption time      23
Action potential      21
Adapted family      197
Algebra(s)      3 4
Algebra(s), sigma      3 4
Algebra(s), sigma, Borel      5
Algebra(s), sigma, completion of      5
Algebra(s), sigma, generated by      4 7
Algebra(s), sigma, independent      13
Algebra(s), sigma, tail      13
Almost sure convergence      14
Almost surely      10
Aperiodic state      68 69
Arley process      121
AS      see “Almost surely”
Backward equation      107
Barrier      42 43
Barrier, absorbing      43
Barrier, elastic      43
Barrier, reflecting      43
Bayes’ formula      11 12
Bernstein equation      270 271
Binary noise      171 184 185
Binomial distribution      8
Birth process      111
Birth process, linear      117
Birth process, pure      111
Birth process, simple      117
Birth rate      111
Birth-death chain      44 52 76 77
Birth-death process      111
Birth-death process, nonhomogeneous      127
Birth-death process, nonlinear      125 129
Blood clotting      123 124
Bochner’s theorem      15
Borel set      5
Borel set in $R^{n}$      4
Borel set, $\sigma$-algebra      4
Borel — Cantelli lemma      5
Borel — Cantelli lemma, first      5
Borel — Cantelli lemma, second      13
Boundary      279
Boundary, accessible      279 280
Boundary, entrance      279
Boundary, exit      279
Boundary, inaccessible      279
Boundary, natural      279
Boundary, regular      279
Branching chain      44 79 203 204 215 216
Brownian motion      160 161 227
Brownian motion with drift      231
Brownian motion, geometric      284
Brownian motion, random walk to      227
Brownian motion, reflected      233
Brownian motion, standard      230
Capocelli — Ricciardi theorem      278 279
Carcinogen      34
Carcinogenesis      14 129
Carcinogenesis, birth-death process in      129
Carcinogenesis, hit in      34
Carcinogenesis, random walk in      34
Central limit theorem      16
Central movement      9
Chapman — Kolmogorov equation      48 106 259
Characteristic function      14 15
Chebyshev inequality      16
Chi-square density      8
Closed set of states      55 131
Closed set of states, minimal      131
Communicating states      55
Complete probability space      5
Completion      5
Compound Poisson process      100
Concordant function      204
Conditional density      12
Conditional density, expectation      12
Conditional density, probability      12
Conditionally independent sequence      209
Contact rate      125
Contagion process      137
Continuous distribution      8
Continuous process      149
Continuous process, Khintchin      260
Continuous process, mean square      152
Continuous process, purely      260
Continuous process, sample path      149
Continuous process, stochastically      148
Continuous process, stochastically, uniformly      148
Convariance      9
Convariance stationary      167
Convergence      14
Convergence in distribution      14
Convergence in probability      14
Convergence in pth mean      14
Convergence, almost sure      14
Convergence, mean square      148
Correlation      9
Counting process      87
Covariance function      146
Darling — Siegert theorem      277
Death process      111
Death process, pure      111 118
Death rate      111
Decomposition, first entrance      54
Decomposition, first step      52
Density function      7
Density function, chi square      9
Density function, conditional      12
Density function, exponential      8
Density function, gamma      8
Density function, joint      7
Depolymerization      21
Differentiation      153
Differentiation, mean square      153
Differentiation, sample path      153
Diffusion coefficient      261
Diffusion process      227 259
Diffusion process with lognormal transitions      281
Diffusion process, Ehrenfests      274
Diffusion process, random walk to      265
Dirac $\delta$-function(al)      251
Distribution function      7
Distribution function, binomial      8
Distribution function, Gaussian      8
Distribution function, geometric      8
Distribution function, joint      7
Distribution function, marginal      7
Distribution function, normal      8
Distribution function, poisson      8
Distribution function, uniform      8
Distribution, initial      40
Distribution, initial, stationary      67
Distribution, initial, steady state      67
Distribution, initial, transition      259
Divergent population      114
Doob — Levy martingale      200
Drift      231
Drift coefficient      261
Ehrenfests chain      45 74
Elastic barriers      43
Electron emission      89
Electron emission in optical detection      99
Embedded chains      132
Entrance boundary      279
Enzyme amplifier system      2
Ergodic process      185
Ergodic properties      131
Ergodic state      68
Ergodic theorem      186
Ergodic theorem, individual      186
Ergodic theorem, mean square      190
Ergodic theorem, strong      186
Events      3
Events, independent      13
Events, prior to a stopping time      220
Exit boundary      279
Exit time      225
Expectation      9
Expectation, conditional      12
Expected duration of the game      28
Expected number of visits      59
Explosive population      114
Exponential density      9
Fatou’s Lemma      11
Feller — Arley process      121
Feller — Lundberg theorem      115
Fibrin      124
Fibrinogen      124
First entrance      54
First entrance, decomposition      54
First entrance, time      131
First passage      31
First passage, probability      31
First passage, probability generation function of      34
First passage, time      33 275
First return time      131
First step decomposition      52
Flat spectrum      252
Fokker — Planck equation      262
Fuchsian equation      282
Furry — Yule process      117
Gambler’s maximum winning      32
Gambler’s maximum winning, ruin      24
Gambler’s maximum winning, ruin, expected time to      28
Gambler’s maximum winning, ruin, probability of      25
Gamma density      8
Gaussian distribution      8
Gaussian process      160
Geometric Brownian motion      284
Geometric distribution      8
Hille’s function      279
Hit in carcinogenesis      34
Hitting time      33 50
Hitting time, mth      54
Holder continuous path      239
Homogeneous Markov chain      40
Impulse response      252
Inaccessible boundary      279
Incubation period      125
Independent events      13
Independent events, $\sigma$-algebras      13
Independent events, random variables      13
Independent increments      87
Independent increments, process with      87
Indicator function      6
Indicator function, random variable      6
Individual ergodic theorem      186
Infected      125
Infectious period      125
Infinitely often      5
Infinitesimal generator      109
Infinitesimal generator, parameter      109
Initial distribution      40
integral      154
Integral, mean square      154
Integral, sample path      153
Intensity function      106
Interarrival time      92
Irreducible class      55
Irreducible class, Markov chain      55
Irreducible class, process      131
Ito integral      254
Jensen’s Inequality      199
Joint density      7
Joint density, distribution      7
Jump process      105
Khintchin stationary      167
Khintchin stationary, continuous process      260
Khintchin stationary, formula      176
Khintchin stationary, theorem      174
Killed process      275
Kolmogorov zero—one law      13
Kolmogorov zero—one law, backward equation      107
Kolmogorov zero—one law, Feller equations      106
Kolmogorov zero—one law, forward equation      107 262
Kolmogorov zero—one law, strong law of large numbers      17
Kolmogorov zero—one law, theorem      151
Laplace transform      15
Latent period      125
Lattice walk      20 41
Law of iterated logarithm      243
Law of Large Numbers      17
Law of Large Numbers, strong      17
Law of large numbers, weak      17
Likelihood ratio      206
Limit inferior      5
Limit inferior, superior      4
Linear birth process      117
Linear death process      118
Lognormal distribution      283
Lognormal distribution, transition      281
Marginal distribution      7
Markov chain      39
Markov chain with stationary transition      40
Markov chain, homogeneous      40
Markov chain, irreducible      55
Markov chain, time reversibility      40
Markov chain, two-state      46
Markov process      106 259
Markov process, strong      51 235 243
Markov time      50
Martingale      195
Martingale, Doob — Levy      200
Martingale, reverse      201
Martingale, stopped      220
Martingale, sub-      196
Martingale, super-      197
Martingale, Wald      206
Maximum winning      32
Mc      see “Markov chain”
Mean recurrence time      62 131
Mean square continuous      152
Mean square continuous, convergence      148
Mean square continuous, differentiability      153
Mean square continuous, distance      146
Mean square continuous, ergodic theorem      189
Mean square continuous, integral      154
Mean value function      98 146
Memoryless random variable      93
Minimal closed set      131
moment      9
Moment, central      9
Moment, mixed      9
Monotone Convergence Theorem      11
Moving average process      167 181
mth hitting time      54
mth return time      54
n-step transition      47
n-step transition, matrix      47
n-step transition, probability      47
Neuron spike activity      89 100
Noise      251
Noise, shot      251
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