A first course in stochastic processes.

Por: Karlin, Samuel, 1923-2007Editor: New York : Academic Press, [1966]Descripción: xi, 502 p. : il. ; 24 cmTema(s): Stochastic processesOtra clasificación: 60-01
Contenidos:
Chapter [1]
ELEMENTS OF STOCHASTIC PROCESSES
1. Review of Basic Terminology and Properties of Random Variables and Distribution Functions [1]
2. Two Simple Examples of Stochastic Processes [11]
3. Classification of General Stochastic Processes [16]
Problems [21]
References [26]
Chapter [2]
MARKOV CHAINS
1. Definitions [27]
2. Examples of Markov Chains [29]
3. Transition Probability Matrices of a Markov Chain [40]
4. Classification of States of a Markov Chain [41]
5. Recurrence [44]
6. Examples of Recurrent Markov Chains [49]
7. More on Recurrence [54]
Problems [55]
References [59]
Chapter [3]
THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND APPLICATIONS
1. Discrete Renewal Equation [61]
2. Proof of Theorem 1.1 [67]
3. Absorption Probabilities [69]
4. Criteria for Recurrence [74]
5. A Queueing Example [76]
6. Another Queueing Model [82]
7. Random Walk [86]
Problems [88]
References [93]
Chapter [4]
ALGEBRAIC METHODS IN MARKOV CHAINS
1. Preliminaries [94]
2. Relations of Eigenvalues and Recurrence Classes [96]
3. Periodic Classes [100]
4. Special Computational Methods in Markov Chains [103]
5. Examples [107]
6. Applications to Coin Tossing [112]
Problems [117]
References [124]
Chapter [5]
RATIO THEOREMS OF TRANSITION PROBABILITIES AND APPLICATIONS
1. Taboo Probabilities [125]
2. Ratio Theorems [127]
3. Existence of Generalized Stationary Distributions [132]
4. Interpretation of Generalized Stationary Distributions [136]
5. Regular, Superregular, and Subregular Sequences for Markov Chains [139]
Problems [145]
References [148]
Chapter [6]
SUMS OF INDEPENDENT RANDOM VARIABLES AS A MARKOV CHAIN
1. Recurrence Properties of Sums of Independent Random Variables [149]
2. Local Limit Theorems [153]
3. Right Regular Sequences for the Markov Chain {Sn} [160]
Problems [170]
References [174]
Chapter [7]
CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS
1. General Pure Birth Processes and Poisson Processes [175]
2. More about Poisson Processes [181]
3. A Counter Model [185]
4. Birth and Death Processes [189]
5. Differential Equations of Birth and Death Processes [192]
6. Examples of Birth and Death Processes [195]
7. Birth and Death Processes with Absorbing States [201]
8. Finite State Continuous Time Markov Chains [206]
Problems [208]
References [217]
Chapter [8]
CONTINUOUS TIME MARKOV CHAINS
1. Differentiability Properties of Transition Probabilities [218]
2. Conservative Processes and the Forward and Backward Differential Equations [223]
3. Construction of a Continuous Time Markov Chain from Its Infinitesimal Parameters [225]
4. Strong Markov Property [230]
Problems [233]
References [235]
Chapter [9]
ORDER STATISTICS, POISSON PROCESSES, AND APPLICATIONS
1. Order Statistics and Their Relation to Poisson Processes [236]
2. The Ballot Problem [244]
3. Empirical Distribution Functions and Order Statistics [250]
4. Some Limit Distributions for Empirical Distribution Functions [256]
Problems [261]
References [270]
Chapter [10]
BROWNIAN MOTION
1. Background Material [271]
2. Joint Probabilities for Brownian Motion [273]
3. Continuity of Paths and the Maximum Variables [276]
Problems [280]
References [285]
Chapter [11]
BRANCHING PROCESSES
1. Discrete Time Branching Processes [286]
2. Generating Function Relations for Branching Processes [288]
3. Extinction Probabilities [290]
4. Examples [294]
5. Two-Type Branching Processes [298]
6. Multi-Type Branching Processes [395]
7. Continuous Time Branching Processes [395]
8. Extinction Probabilities for Continuous Time Branching Processes [319]
9. Limit Theorems for Continuous Time Branching Processes [313]
10. Two-Type Continuous Time Branching Process [318]
11. Branching Processes with General Variable Lifetime [325]
Problems [339]
References [335]
Chapter [12]
COMPOUNDING STOCHASTIC PROCESSES
1. Multidimensional Homogeneous Poisson Processes [337]
2. An Application of Multidimensional Poisson Processes to Astronomy [344]
3. Immigration and Population Growth [345]
4. Stochastic Models of Mutation and Growth [348]
5. One-Dimensional Geometric Population Growth [353]
6. Stochastic Population Growth Model in Space and Time [356]
7. Deterministic Population Growth with Age Distribution [360]
8. A Discrete Aging Model [366]
Problems [367]
References [372]
Chapter [13]
DETERMINISTIC AND STOCHASTIC GENETIC AND ECOLOGICAL PROCESSES
1. Genetic Models; Description of the Genetic Mechanism [373]
2. Inbreeding [382]
3. Polyploidy [388]
4. Markov Processes Induced by Direct Product Branching Processes [390]
5. Multi-Type Population Frequency Models [396]
6. Eigenvalues of Markov Chains Induced by Direct Product Branching Processses [399]
7. Eigenvalues of Multi-Type Mutation Model [407]
8. Probabilistic Interpretations of the Eigenvalues [417]
Problems [425]
References [429]
Chapter [14]
QUEUEING PROCESSES
1. General Description [430]
2. The Simplest Queueing Processes (M/M/1) [431]
3. Some General One-Server Queueing Models [433]
4. Embedded Markov Chain Method Applied to the Queueing Model (M/GI/1) [439]
5. Exponential Service Times (G/M/l) [445]
6. Gamma Arrival Distribution and Generalizations (Ek/M/l) [448]
1. Exponential Service with s Servers (GI/M/s) [453]
8. The Virtual Waiting Time and the Busy Period [455]
Problems [462]
References [468]
APPENDIX. REVIEW OF MATRIX ANALYSIS
1. The Spectral Theorem [469]
2. The Frobenius Theory of Positive Matrices [475]
MISCELLANEOUS PROBLEMS [485]
Index [499]
DIAGRAM OF LOGICAL DEPENDENCE OF CHAPTERS
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SEMINARIO DE PROCESOS ESTOCÁSTICOS


Incluye referencias bibliográficas.

Chapter [1] --
ELEMENTS OF STOCHASTIC PROCESSES --
1. Review of Basic Terminology and Properties of Random Variables and Distribution Functions [1] --
2. Two Simple Examples of Stochastic Processes [11] --
3. Classification of General Stochastic Processes [16] --
Problems [21] --
References [26] --
Chapter [2] --
MARKOV CHAINS --
1. Definitions [27] --
2. Examples of Markov Chains [29] --
3. Transition Probability Matrices of a Markov Chain [40] --
4. Classification of States of a Markov Chain [41] --
5. Recurrence [44] --
6. Examples of Recurrent Markov Chains [49] --
7. More on Recurrence [54] --
Problems [55] --
References [59] --
Chapter [3] --
THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND APPLICATIONS --
1. Discrete Renewal Equation [61] --
2. Proof of Theorem 1.1 [67] --
3. Absorption Probabilities [69] --
4. Criteria for Recurrence [74] --
5. A Queueing Example [76] --
6. Another Queueing Model [82] --
7. Random Walk [86] --
Problems [88] --
References [93] --
Chapter [4] --
ALGEBRAIC METHODS IN MARKOV CHAINS --
1. Preliminaries [94] --
2. Relations of Eigenvalues and Recurrence Classes [96] --
3. Periodic Classes [100] --
4. Special Computational Methods in Markov Chains [103] --
5. Examples [107] --
6. Applications to Coin Tossing [112] --
Problems [117] --
References [124] --
Chapter [5] --
RATIO THEOREMS OF TRANSITION PROBABILITIES AND APPLICATIONS --
1. Taboo Probabilities [125] --
2. Ratio Theorems [127] --
3. Existence of Generalized Stationary Distributions [132] --
4. Interpretation of Generalized Stationary Distributions [136] --
5. Regular, Superregular, and Subregular Sequences for Markov Chains [139] --
Problems [145] --
References [148] --
Chapter [6] --
SUMS OF INDEPENDENT RANDOM VARIABLES AS A MARKOV CHAIN --
1. Recurrence Properties of Sums of Independent Random Variables [149] --
2. Local Limit Theorems [153] --
3. Right Regular Sequences for the Markov Chain {Sn} [160] --
Problems [170] --
References [174] --
Chapter [7] --
CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS --
1. General Pure Birth Processes and Poisson Processes [175] --
2. More about Poisson Processes [181] --
3. A Counter Model [185] --
4. Birth and Death Processes [189] --
5. Differential Equations of Birth and Death Processes [192] --
6. Examples of Birth and Death Processes [195] --
7. Birth and Death Processes with Absorbing States [201] --
8. Finite State Continuous Time Markov Chains [206] --
Problems [208] --
References [217] --
Chapter [8] --
CONTINUOUS TIME MARKOV CHAINS --
1. Differentiability Properties of Transition Probabilities [218] --
2. Conservative Processes and the Forward and Backward Differential Equations [223] --
3. Construction of a Continuous Time Markov Chain from Its Infinitesimal Parameters [225] --
4. Strong Markov Property [230] --
Problems [233] --
References [235] --
Chapter [9] --
ORDER STATISTICS, POISSON PROCESSES, AND APPLICATIONS --
1. Order Statistics and Their Relation to Poisson Processes [236] --
2. The Ballot Problem [244] --
3. Empirical Distribution Functions and Order Statistics [250] --
4. Some Limit Distributions for Empirical Distribution Functions [256] --
Problems [261] --
References [270] --
Chapter [10] --
BROWNIAN MOTION --
1. Background Material [271] --
2. Joint Probabilities for Brownian Motion [273] --
3. Continuity of Paths and the Maximum Variables [276] --
Problems [280] --
References [285] --
Chapter [11] --
BRANCHING PROCESSES --
1. Discrete Time Branching Processes [286] --
2. Generating Function Relations for Branching Processes [288] --
3. Extinction Probabilities [290] --
4. Examples [294] --
5. Two-Type Branching Processes [298] --
6. Multi-Type Branching Processes [395] --
7. Continuous Time Branching Processes [395] --
8. Extinction Probabilities for Continuous Time Branching Processes [319] --
9. Limit Theorems for Continuous Time Branching Processes [313] --
10. Two-Type Continuous Time Branching Process [318] --
11. Branching Processes with General Variable Lifetime [325] --
Problems [339] --
References [335] --
Chapter [12] --
COMPOUNDING STOCHASTIC PROCESSES --
1. Multidimensional Homogeneous Poisson Processes [337] --
2. An Application of Multidimensional Poisson Processes to Astronomy [344] --
3. Immigration and Population Growth [345] --
4. Stochastic Models of Mutation and Growth [348] --
5. One-Dimensional Geometric Population Growth [353] --
6. Stochastic Population Growth Model in Space and Time [356] --
7. Deterministic Population Growth with Age Distribution [360] --
8. A Discrete Aging Model [366] --
Problems [367] --
References [372] --
Chapter [13] --
DETERMINISTIC AND STOCHASTIC GENETIC AND ECOLOGICAL PROCESSES --
1. Genetic Models; Description of the Genetic Mechanism [373] --
2. Inbreeding [382] --
3. Polyploidy [388] --
4. Markov Processes Induced by Direct Product Branching Processes [390] --
5. Multi-Type Population Frequency Models [396] --
6. Eigenvalues of Markov Chains Induced by Direct Product Branching Processses [399] --
7. Eigenvalues of Multi-Type Mutation Model [407] --
8. Probabilistic Interpretations of the Eigenvalues [417] --
Problems [425] --
References [429] --
Chapter [14] --
QUEUEING PROCESSES --
1. General Description [430] --
2. The Simplest Queueing Processes (M/M/1) [431] --
3. Some General One-Server Queueing Models [433] --
4. Embedded Markov Chain Method Applied to the Queueing Model (M/GI/1) [439] --
5. Exponential Service Times (G/M/l) [445] --
6. Gamma Arrival Distribution and Generalizations (Ek/M/l) [448] --
1. Exponential Service with s Servers (GI/M/s) [453] --
8. The Virtual Waiting Time and the Busy Period [455] --
Problems [462] --
References [468] --
APPENDIX. REVIEW OF MATRIX ANALYSIS --
1. The Spectral Theorem [469] --
2. The Frobenius Theory of Positive Matrices [475] --
MISCELLANEOUS PROBLEMS [485] --
Index [499] --
DIAGRAM OF LOGICAL DEPENDENCE OF CHAPTERS --

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