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本教材試圖從工科的角度介紹隨機過程的基本概念和方法內容，特點是閱讀的起點相對較低，使讀者能夠在較短的時間內瞭解隨機過程的基礎知識和主要內容，首先對於隨機過程的基本思想進行詳細的介紹，隨後選擇幾種重要的隨機過程進行重點介紹，而對於涉及較深數學知識的內容列出文獻，便於感興趣的讀者進行追蹤學習。
目次
Preface
Chapter 1 Basis of probability
1.1 Random ovcnts
1.1.1 Random experiments
1.1.3 Calculation among random evcnts
1.1.4 u-algebras
1.2 Probability
1.2.1 What is probability
1.2.2 Properties of probability
1.2.3 Two fundamental probability models
1.2.4 Conditional probability and three important formulas
1.2.5 Independence of events
1.3 Random variables
1.3.1 Definition
1.3.2 Cumulative distribution functions
1.3.4 Multiple-dimensional random variablcs
1.3.5 Distributions of functions of random variables
1.3.6 Conditional distributions and indepenclences
1.3.7 Order statistics
1.4 Numerical characteristics
1.4.1 Definition of mathematical expectations
1.4.2 Properties
1.4.3 0ther numerical characteristics of random variables
1.4.4 Conditional mathematical expectations
1.5 Limiting thcoroms
1.5.1 Convcrgencc of random variablcs
1.5.2 Law of large numbers
1.5.3 Central limit thcorcms
Exercise 1
Answers or tips for Exercise 1
Chapter 2 Stochastic processes
2.1 Definition and classification
2.1.1 Definition
2.1.3 Examples
2.2 Statistical laws of stochastic processes
2.2.1 Finite dimensional distribution functions
2.2.2 Kolmogorov's theorem
2.3 Mcasurcmcnts of stochastic proccsscs
2.3.1 Measurements for one stochastic process
2.3.2 Measurements for two stochastic processes
2.4 Further comments
Exercise 2
Answers or tips for Exercise 2
Chapter 3 Poisson processes
3.1 Definition and measurements
3.1.1 Definition
3.1.2 Measurements
3.2 Waiting timcs and intcrarrival times
3.2.1 Waiting times
3.2.2 Interarrival times
3.3 Conditional distributions
3.4 Extcnsions of Poisson procosscs
3.4.1 Non-homogencous Poisson proccsscs
3.4.2 Compound Poisson processes
3.4.3 Conditional Poisson processes
3.4.4 Renewal processes
Exercise 3
Answers or tips for Exercise 3
Chapter 4 Discrete-time Markov chains
4.1 Definition of discrete-time Markov chains
4.1.1 Definition
4.1.2 Chapman-Kolmogorov equations
4.2 Finite-dhnensional distributions
4.3 Propcrtios of a singlo statc
4.3.2 Transience and recurrence
4.4 Decomposition of state space
4.4.1 Equivalencc rclation
4.4.2 Decomposition of statc space
4.5 Asymptotic behaviors of transition probabilities pij(n)
4.5.1 Case one: state j is transient or -recurrent
4.5.2 Case two: state j is positive-recurrent
4.6 Stationary distributions
4.6.1 Definition of stationary distributions
4.6.2 How many stationary distributions a Markov chain may have?
4.6.3 Rates of convergence to stationary distributions
4.6.4 Stationary distributions of a ccnsored Markov chain
4.6.5 Quasi-stationary distributions
4.7 Rovcrsiblc Markov chains
Exercise 4
Answers or tips for Exercise 4
Chapter 5 Continuous-time Markov chains
5.1 Dofinitionof continuous-timc Markov chains
5.1.1 Definition
5.1.2 Chapman-Kolmogorov equations
5.2 Finite-dhnensional distributions
5.3 Q-matriccs
5.4 Kolmogorov difforcntial cquations
5.5 Asymptotic behaviors
5.5.1 Transience and recurrence
5.5.2 Limiting results
5.5.3 Stationary distributions
5.6 Birth and death processes
Exercise 5
Answers or tips for Exercise 5
Chapter 6 Simple Markovian queueing models
6.1 Torminology and notation
6.2 Little's law and PASTA property
6.2.1 Little's law
6.2.2 PASTA property
6.3 M/M/l queueing model
6.3.1 Stationary distribution of queue length
6.3.2 Distributions of sojourn times and waiting times
6.3.3 Busy period distribution
6.3.4 Departure process
6.4 M/M/n, and state dependent M/M/l queueing model
6.4.1 M/M/n, queucing modcl
6.4.2 State dcpendentM/M/lqueucing modcl
6.5 Mx/M/l queueing model
6.6 M/G/l queueing model
6.6.1 Embedded Markov chain
6.6.2 M/Er/1 qucueing model
Exercise 6
Answers or tips for Exercise 6
Chapter 7 Stationary processes
7.1.1 Strict-sense stationary processes
7.1.2 Wide-sense stationary processes
7.2 Analytic propcrties of wide-sonso stationary proccsscs
7.3 Corrclation functions and their spectra
7.3.1 Properties of correlation functions
7.3.2 Spectral density functions
7.3.3 Properties of spectral density functions
7.3.4 Continuous-time whitc noisc processes
7.5 Passing through a linear time-invariant system
Exercise 7
Answers or tips for Exercise 7
References
Indes
Chapter 1 Basis of probability
1.1 Random ovcnts
1.1.1 Random experiments
1.1.3 Calculation among random evcnts
1.1.4 u-algebras
1.2 Probability
1.2.1 What is probability
1.2.2 Properties of probability
1.2.3 Two fundamental probability models
1.2.4 Conditional probability and three important formulas
1.2.5 Independence of events
1.3 Random variables
1.3.1 Definition
1.3.2 Cumulative distribution functions
1.3.4 Multiple-dimensional random variablcs
1.3.5 Distributions of functions of random variables
1.3.6 Conditional distributions and indepenclences
1.3.7 Order statistics
1.4 Numerical characteristics
1.4.1 Definition of mathematical expectations
1.4.2 Properties
1.4.3 0ther numerical characteristics of random variables
1.4.4 Conditional mathematical expectations
1.5 Limiting thcoroms
1.5.1 Convcrgencc of random variablcs
1.5.2 Law of large numbers
1.5.3 Central limit thcorcms
Exercise 1
Answers or tips for Exercise 1
Chapter 2 Stochastic processes
2.1 Definition and classification
2.1.1 Definition
2.1.3 Examples
2.2 Statistical laws of stochastic processes
2.2.1 Finite dimensional distribution functions
2.2.2 Kolmogorov's theorem
2.3 Mcasurcmcnts of stochastic proccsscs
2.3.1 Measurements for one stochastic process
2.3.2 Measurements for two stochastic processes
2.4 Further comments
Exercise 2
Answers or tips for Exercise 2
Chapter 3 Poisson processes
3.1 Definition and measurements
3.1.1 Definition
3.1.2 Measurements
3.2 Waiting timcs and intcrarrival times
3.2.1 Waiting times
3.2.2 Interarrival times
3.3 Conditional distributions
3.4 Extcnsions of Poisson procosscs
3.4.1 Non-homogencous Poisson proccsscs
3.4.2 Compound Poisson processes
3.4.3 Conditional Poisson processes
3.4.4 Renewal processes
Exercise 3
Answers or tips for Exercise 3
Chapter 4 Discrete-time Markov chains
4.1 Definition of discrete-time Markov chains
4.1.1 Definition
4.1.2 Chapman-Kolmogorov equations
4.2 Finite-dhnensional distributions
4.3 Propcrtios of a singlo statc
4.3.2 Transience and recurrence
4.4 Decomposition of state space
4.4.1 Equivalencc rclation
4.4.2 Decomposition of statc space
4.5 Asymptotic behaviors of transition probabilities pij(n)
4.5.1 Case one: state j is transient or -recurrent
4.5.2 Case two: state j is positive-recurrent
4.6 Stationary distributions
4.6.1 Definition of stationary distributions
4.6.2 How many stationary distributions a Markov chain may have?
4.6.3 Rates of convergence to stationary distributions
4.6.4 Stationary distributions of a ccnsored Markov chain
4.6.5 Quasi-stationary distributions
4.7 Rovcrsiblc Markov chains
Exercise 4
Answers or tips for Exercise 4
Chapter 5 Continuous-time Markov chains
5.1 Dofinitionof continuous-timc Markov chains
5.1.1 Definition
5.1.2 Chapman-Kolmogorov equations
5.2 Finite-dhnensional distributions
5.3 Q-matriccs
5.4 Kolmogorov difforcntial cquations
5.5 Asymptotic behaviors
5.5.1 Transience and recurrence
5.5.2 Limiting results
5.5.3 Stationary distributions
5.6 Birth and death processes
Exercise 5
Answers or tips for Exercise 5
Chapter 6 Simple Markovian queueing models
6.1 Torminology and notation
6.2 Little's law and PASTA property
6.2.1 Little's law
6.2.2 PASTA property
6.3 M/M/l queueing model
6.3.1 Stationary distribution of queue length
6.3.2 Distributions of sojourn times and waiting times
6.3.3 Busy period distribution
6.3.4 Departure process
6.4 M/M/n, and state dependent M/M/l queueing model
6.4.1 M/M/n, queucing modcl
6.4.2 State dcpendentM/M/lqueucing modcl
6.5 Mx/M/l queueing model
6.6 M/G/l queueing model
6.6.1 Embedded Markov chain
6.6.2 M/Er/1 qucueing model
Exercise 6
Answers or tips for Exercise 6
Chapter 7 Stationary processes
7.1.1 Strict-sense stationary processes
7.1.2 Wide-sense stationary processes
7.2 Analytic propcrties of wide-sonso stationary proccsscs
7.3 Corrclation functions and their spectra
7.3.1 Properties of correlation functions
7.3.2 Spectral density functions
7.3.3 Properties of spectral density functions
7.3.4 Continuous-time whitc noisc processes
7.5 Passing through a linear time-invariant system
Exercise 7
Answers or tips for Exercise 7
References
Indes
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