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Kao E. — Introduction to Stochastic Processes

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Название: Introduction to Stochastic Processes

Автор: Kao E.

Аннотация:

Intended for a calculus-based course in stochastic processes at the graduate or advanced undergraduate level, this text offers a modern, applied perspective.
Instead of the standard formal and mathematically rigorous approach usual for texts for this course, Edward Kao emphasizes the development of operational skills and analysis through a variety of well-chosen examples.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 438

Добавлена в каталог: 19.04.2008

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Предметный указатель

Recurrence time of discrete-time Markov chain      169
Recurrence time, mean, of a discrete-time Markov chain      175
Recurrence time, mean, of a Markov renewal process      337
Recurrent state of a Markov renewal process      336
Regeneration cycle      132—144
Regenerative approach for simulation      135—136
Regenerative process      132—133 253 338
Regenerative reward process      133
Renewal density      99
Renewal function      99 107
Renewal function for phase-type renewal process      273
Renewal process      98
Renewal process with exponential interarrival times      117—118
Renewal process with uniform interarrival times      110—112 157—159
Renewal process, alternating      118—121
Renewal process, arrival times of      98
Renewal process, asymptotic expansion of renewal function      101
Renewal process, asymptotic mean and variance of number of renewals      128
Renewal process, asymptotic rate of renewal      101
Renewal process, delayed      129 335
Renewal process, lifetime of      131
Renewal process, stationary      129—130
Renewal process, transient      130—131 336
Renewal reward process      118
Renewal-type equation      101 128 331—336
Replacement models, age replacement policy      124—127
Replacement models, block replacement policy      122—123
Replacement models, opportunity-based block replacement      150
Replacement models, repair Limit replacement method      344—346
Replacement models, semi-Markovian deterioration      364
Residual life      see "Excess life"
Reversed Markov chain, continuous-time      285 291—292
Reversed Markov chain, discrete-time      208
Reversible Markov chain, continuous-time      284—288
Reversible Markov chain, discrete-time      207—210
Reversible Markov chain, Kolmogorov criteria      209—210 285
Reversible Markov chain, two-dimensional      287
Riemann — Stieltjes integral      29—34
Right-continuous function      28
Ruin problem      see "Insurance problem"
Sample path      3
Sample path of a Brownian motion      376
Sample path of a continuous-time Markov chain      240
Second factorial moment      8
Semi-Markov kernel      323 326 328—330 351
Semi-Markov process      339—341
Semi-Markov process, excess life and age      355
Semi-Markov process, expected sojourn time      342—343
Semi-Markov reward process      343—344
Semi-regenerative process      348—349 351—352
Skip-free-to-the-left property      262
Stable state      241
Starting state probability vector      162 240
State probability vector of continuous-time Markov chain      240
State probability vector of discrete-time Markov chain      166

State probability vector, solution by uniformization      275—276
State reduction      201 233
State space      2
Stationary distribution of continuous-time Markov chain      254
Stationary distribution of discrete-time Markov chain      176
Stationary increments      4 49 51 400
Stationary renewal process      see "Renewal process"
statistical process control      149
Stochastic differential equations      396
Stochastic differential equations, control of      409—417
Stochastic process      2
Stopping time      104 125 351 385
Strong Markov property      162 200 241 385
Substochastic matrix      203 222
Taboo set      220
Tail probability      39
Tandem queue      69—71 288—289
Taylor series expansion      36—37
Time average      35
Time domain      7
Time homogeneous, continuous-time Markov chain      240
Time homogeneous, discrete-time Markov chain      162
Time homogeneous, infinite horizon, discounted problem      413—414
Time homogeneous, Markov renewal process      323
Time in transient states of continuous-time Markov chain      258
Time in transient states of discrete-time Markov chain      194—195
Total life, or spread, or recurrence time      107
Total life, or spread, or recurrence time, distribution      115
Total life, or spread, or recurrence time, limiting distribution      117
Traffic equation      290 293
Trailing stops      142
Transform domain      7
Transience of Markov chain necessary and sufficient condition for      188
Transient state      169 336
Transition diagram      178 243 286
Transition function      240
Transition function of semi-Markov process      339—340
Transition function of two-state Markov chain, closed form      247
Transition function of Yule process, closed form      249—251
Transition rates      241
Truncated reversible Markov chain      287
Two machine transfer line      299
Two-dimensional Poisson process      see "Poisson process"
Two-dimensional transform      27
Uniformization      273—274
Variance parameter of a Brownian motion      376
Variance to mean ratio      73 76
Variance-covariance matrix      411
Virtual delay in queue      388
Virtual transition      273 279
Wald's equation      104 125 137
Weibull distribution      205—206 270—271 324—325
Wiener process      see "Brownian motion"
Yule process      249—251
z-transform      see "Generating function"

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