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Kao E. Ч Introduction to Stochastic Processes
Kao E. Ч Introduction to Stochastic Processes

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Ќазвание: Introduction to Stochastic Processes

јвтор: Kao E.

јннотаци€:

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.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2002

 оличество страниц: 438

ƒобавлена в каталог: 19.04.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$M(t)/G/\infty$ queue      91
$M(t)/M/1/4$ queue      67Ч68
$M(t)/M/s$ queue      65Ч67
$M/G/\infty$ queue, departure process      68Ч69 82Ч83
$M/H_{2}/1$ queue, waiting time, distribution of      25Ч26
$M/M/\infty$ queue, time dependent probability      90
Absorbing state      174 241
Accessibility      172
Alternating renewal process      see "Renewal process"
Aperioidic state and chain      171
Arbitrage      402
Arrival theorem      see "Closed queueing network"
Asymptotic-rate theorem      27 42 100
Balance equation      see also "Detailed balance equation"
Balance equation for continuous-time Markov chain      253Ч254
Balance equation for discrete-time Markov chain      177Ч179
Bellman's functional equation      409
Beta of a security      407
Birth and death process      242Ч243 254Ч255 260Ч263
Birth rates      242
Black Ч Scholes differential equation      402Ч403
Blackwell's renewal theorem      128
Branching process      40Ч41
Brownian motion      374Ч375
Brownian motion, arithmetic      397 399
Brownian motion, geometric      398Ч401
Brownian motion, integrated      417
Brownian motion, reflected at origin      419
Brownian motion, standard      394
Brownian motion, with two barriers      384Ч385
Call option, European      403Ч404
Canonical form of Markov chain      173 185Ч186
Capital asset pricing      407Ч409
Cash management problem      190Ч192 214 282Ч284
Censored discrete-time Markov chain      200Ч201
Central limit theorem      128 401
Central server model      306
Cesaro limit      see "Time average"
Chapman Ч Kolmogorov equation of continuous-time Markov chain      240
Chapman Ч Kolmogorov equation of diffusion process      385Ч386
Chapman Ч Kolmogorov equation of discrete-time Markov chain      165Ч166
Characteristic function      28
Closed queueing network      293Ч294 308
Closed queueing network with blocking      296 314Ч315
Closed queueing network, arrival theorem for      295
Closed queueing network, Buzen's algorithm      294Ч295 320
Closed queueing network, normalizing constant      294
Closed queueing network, product form solution      294
Closed queueing network, waiting time at server      295
Coefficient of variation      73 305
Communication      168
Compering exponential      19Ч21 242 350
Compound random variable      10
Compound random variable, generating function      10
Compound random variable, mean and variance      10Ч11
Contingent claim      402
Continuous distribution, random variable, $H_{2}$ with balanced means      25 305
Continuous distribution, random variable, bivariate normal      408
Continuous distribution, random variable, Erlang      21
Continuous distribution, random variable, exponential      19
Continuous distribution, random variable, gamma      21 123 126
Continuous distribution, random variable, generalized Erlang      267
Continuous distribution, random variable, hyperexponential      268
Continuous distribution, random variable, mixture of generalized Erlang      269
Continuous distribution, random variable, mixture of two Erlang      305
Continuous distribution, random variable, multivariate normal      395
Continuous distribution, random variable, normal      281 386 400 403
Continuous distribution, random variable, Weibull      205Ч206
Continuous-time Markov chain      239
Continuous-time Markov chain as Markov renewal process      331
Continuous-time Markov chain of QBD type      309Ч310
Continuous-time Markov chain two-dimensional      306
Continuous-time Markov chain, absorbing chains      256Ч258
Continuous-time Markov jump process      276
Convolution      18 335
Counting process      5
Coupon collection problem      199Ч200
Covariance      395 417
Current life, or age, or backward recurrence time      107
Current life, or age, or backward recurrence time, distribution of      114Ч115
Data base management      89 219 381Ч382
Death rates      242
Defective random variable      130 170
Delayed renewal process      see "Renewal process"
Denumerable Markov chain      162
Derivative security      402
Detailed balance equation of reversible Markov chain      209
Diffusion equations for Brownian motion, backward equation      376Ч377
Diffusion equations for Brownian motion, forward equation      377Ч378 418
Diffusion process      385
Diffusion process with reflecting barrier      386
Diffusion process, generalized      391Ч393
Diffusion process, limiting density      392
Directly Riemann integrable      102 120
Discounted reward      203 277Ч280
Discrete distribution, random variable, binomial      8
Discrete distribution, random variable, generalized negative binomial      198Ч199
Discrete distribution, random variable, geometric      9 11 130 171
Discrete distribution, random variable, negative binomial      9
Discrete distribution, random variable, Poisson      8
Discrete renewal process      144Ч146
Discrete renewal process, delayed      171
Discrete renewal process, excess life      145Ч146
Discrete renewal process, limiting excess life      211Ч212
Discrete-time Markov chain      162
Discrete-time Markov chain of GI/M/1 type      223
Discrete-time Markov chain of QBD type      221
Discrete-time Markov chain, absorbing chain      173Ч174 188Ч190
Discrete-time Markov chain, classification of state      167Ч169
Discrete-time Markov chain, decomposition of state space      172Ч173 229Ч230
Discrete-time Markov chain, embedded in a continuous-time Markov chain      242 274
Discrete-time Markov chain, embedded in a Markov renewal process      337 343
Discrete-time Markov chain, equivalence class      168
Discrete-time Markov chain, n-step transition probability      165
Discrete-time process      2
Drift of a Brownian motion      376
Elementary renewal theorem      101 128
Equilibrium renewal process      see "Stationary renewal process"
Ergodic discrete-time Markov chain      175Ч176
Erlang loss formula      288
Excess life, or residual life, or forward recurrence time      107
Excess life, or residual life, or forward recurrence time under semi-regenerative process paradigm      349
Excess life, or residual life, or forward recurrence time, distribution of      109
Excess life, or residual life, or forward recurrence time, limiting distribution of      110
Excess life, or residual life, or forward recurrence time, limiting mean excess life      110
Excess life, or residual life, or forward recurrence time, time average of expected excess life      127
Filtered nonhomogeneous Poisson process      91
Filtered Poisson process      76Ч80
Filtered Poisson process, mean and variance for      79
Filtered Poisson process, probability generation function for      79
Filtered Poisson process, response function of      77
Final value property of generating function      6 35 41
Final value property of Laplace transform      18 35 41
First passage time of Brownian motion      379Ч380 395 419
First passage time of discrete-time Markov chain      168Ч169 175 190
Flexible manufacturing system      296Ч297 306Ч308 365Ч366
Fork Join queue      308
Forward contract      401Ч403
Function of bounded variation      31
Fundamental matrix of continuous-time Markov chain      257
Fundamental matrix of discrete-time Markov chain      189
Gain rate      203 277
Gamma function      21
Gauss kernel      418
Gaussian process      395
Generating function      6 294
Generating function, finding moments      8
Generating function, numerical inversion      16Ч17 44Ч45
Geometric transform      see "Generating function"
GI/G/1 queue, diffusion approximation      386Ч389
GI/G/c queue, diffusion approximation      393Ч394
GI/M/1 queue under Markov renewal paradigm      329
GI/M/1 queue, limiting probabilities      181Ч183
GI/M/1 queue, queue length distribution      359Ч362
GI/M/c queue queue      86Ч87
Gordon Ч Newell network      see "Closed queueing network"
Hamilton Ч Jacobi Ч Bellman equation      411Ч412 414Ч416
Holding time distribution      323
Holding time distribution, mean      337
Independent increments      4 49 51 400
Index bond, Fisher's model of      405Ч407
Index set      2
Infinitesimal generator      242
Instantaneous state      241
Insurance problem      21Ч24
Integrate intensity function      56
Intensity function      56
Inventory models      88
Inventory models, (S-1,S) policy      90
Inventory models, continuous review (s,S) policy      120
Inventory models, continuous review, unit demand      147Ч148
Inventory models, discrete-time with batch demands      346Ч347
Inventory models, periodic review (s,S) policy      113 149 164 167 204
Inventory models, two-echelon repairable item      312Ч313
Irreducible Markov chain      168
Ito's lemma, process      398Ч399 404Ч405
Jackson network      see "Open Jackson network"
Jensen's inequality      407
Kelly's lemma      289
Key renewal theorem      102
Kolmogorov criteria      see "Reversible Markov chain"
Kolmogorov differential equations, backward      245Ч246
Kolmogorov differential equations, forward      246 265
Kolmogorov differential equations, Laplace transform      246Ч247 265
Lack of anticipation assumption (LAA)      85
Laplace transform      17
Laplace transform of renewal function      99Ч100
Laplace transform, finding moments      18
Laplace transform, numerical inversion      25 26 45Ч46
Laplace Ч Stieltjes transform      32Ч34 331
Laws of total probability      12 19 103 331 351
Left limit      28
Leibnitz's rule      35Ч36
Length biased sampling      108 157
Limiting state probability of continuous-time Markov chain      252Ч254
Limiting state probability of discrete-time Markov chain      175Ч178 233
Limiting state probability of Markov renewal process      338
Limiting state probability, solution by state reduction      201Ч203
Little's formula      140Ч141 293
Little-oh function      20 22Ч23 34Ч35 65Ч66
M/G/1 queue under Markov renewal paradigm      325Ч327
M/G/1 queue with group arrivals      366
M/G/1 queue, control with an N policy      138Ч140 366
M/G/1 queue, Laplace Ч Stieltjes transform of sojourn time      223
M/G/1 queue, limiting probabilities      180Ч181
M/G/1 queue, Pollaczek Ч Khintchine formula      218
M/G/1 queue, queue length distribution      136Ч138 350Ч351 357Ч359
M/G/1 queue, special service after an idle period      366
M/G/c queue      86
M/M/1 queue      263
M/M/3 queue, departure process of      327Ч328
M/M/s queue      244 255Ч256 263Ч264 285Ч286
M/M/s/s queue      287Ч288
M/PH/1 queue      224 310
Marked Poisson process      see "Poisson process"
Markov chain subordinated to a Poisson process      273 278
Markov jump process with reward      277Ч282
Markov process      385
Markov renewal equation      336
Markov renewal equation, limiting solution      339
Markov renewal function      331Ч336
Markov renewal process      323
Markov renewal process, embedded in semi-Markov process      339Ч340
Markov renewal process, embedded in semi-regenerative process      348Ч351
Markov renewal type of equation      352
Markov reward processes, continuous-time      277Ч281
Markov reward processes, discrete-time      203
Markovian property      162
Matrix exponential      247Ч248 251
Maximum likelihood estimator      62
Mean holding time      337
Mean value function      57
Memory less property      21 241
Merton's Portfolio selection problem      398 415Ч417
Method of embedding      164
Moment generating function      27
Moment generating function of normal distribution      28
Multiprogramming system      390Ч391
Nonhomogeneous Poisson process      56Ч58
Nonhomogeneous Poisson process, arrival time condition on arrival count      58Ч59
Nonhomogeneous Poisson process, filtered      see "Filtered nonhomogeneous Poisson process"
Nonhomogeneous Poisson process, transform arrival time to that of Poisson      60Ч61
Nonstationary Poisson process      see "Nonhomogeneous Poisson process"
Null recurrent state      169 175
Occupancy-time statistics of continuous-time Markov chain      257Ч258
Occupancy-time statistics of discrete-time Markov chain      171 189
Open Jackson network      290Ч293
Open Jackson network, product form solution      291
Ornstein Ч Uhlenbeck process      417
Palm theorem      56
Palm theorem, with nonhomogeneous Poisson arrivals      91
Partial fraction expansion      14
Periodic discrete-time Markov chain      176
Periodic discrete-time Markov chain, canonical form of      185Ч188 232Ч233
Periodicity of discrete-time Markov chain      171
Perpetual warrant      382Ч383
PH/M/1 queue      224
PH/M/c queue      311Ч312
Phase-type distribution, approximation by      270Ч271
Phase-type distribution, continuous-time      264Ч266 361Ч362 387
Phase-type distribution, convolution      266Ч267
Phase-type distribution, discrete-time      197Ч198
Phase-type distribution, limiting excess-life distribution      311
Phase-type distribution, moments      266
Phase-type distribution, order of      265
Phase-type renewal process      271Ч273
Pointwise limit      35
Poisson arrival see time averages (PASTA)      83Ч87
Poisson arrival see time averages (PASTA), applied to GI/M/c queue      86Ч87
Poisson arrival see time averages (PASTA), applied to M/G/1 queue      137 359
Poisson process      48
Poisson process as a birth and death process      244
Poisson process, arrival time condition on arrival count      52Ч53
Poisson process, compound      72Ч76
Poisson process, decomposition      54
Poisson process, generating arrival count by simulation      52
Poisson process, generating arrival times by simulation      52
Poisson process, interarrival time of      51
Poisson process, logarithmic Poisson      74Ч75
Poisson process, marked      80
Poisson process, stuttering Poisson      75Ч76
Poisson process, two-dimensional      80Ч83
Positive recurrence      169 175
Probability generating function      7
Probability generating function, finding moments      8
Product form solution, nonexistence of      296
Product warranty problems      112 148
Pure birth process      304
Quality control      183Ч185
Quasi birth and death (QBD) process      222
Queueing network with blocking      315
R matrix of QBD process      272
Random sum      see "Compound random variable"
Random walk      221
Random walk with a reflecting barrier      179
Random walk, approximate a Brownian motion      374Ч375
Random walk, Markov chain formulation      220Ч221
Random walk, simple      41 104Ч105 150Ч151
rcll      29
Recurrence time of a renewal process      see "Total life"
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