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
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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
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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
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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 null-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
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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
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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
, and state dependent M/M/l queueing model
6.4.1 M/M
, 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
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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
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References
Indes

本教材试图从工科的角度介绍随机过程的基本概念和方法内容，特点是阅读的起点相对较低，使读者能够在较短的时间内了解随机过程的基础知识和主要内容，首先对于随机过程的基本思想进行详细的介绍，随后选择几种重要的随机过程进行重点介绍，而对于涉及较深数学知识的内容列出