A first course in stochastic processes.
Editor: New York : Academic Press, [1966]Descripción: xi, 502 p. : il. ; 24 cmTema(s): Stochastic processesOtra clasificación: 60-01Chapter [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
Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
---|---|---|---|---|---|---|---|---|
Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 60 K18 (Browse shelf) | Available | A-2243 |
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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