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| Kannan D. — An introduction to stochastic processes |
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| Предметный указатель |
 -algebra(s) 3
-algebra(s), Borel 4
-algebra(s), generated by a random vector 8
-algebra(s), independent 13
-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  4
Borel set, -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  -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, -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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