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外国人扫描的STOCHASTIC PROCESS by Sheldon Ross 2nd
chapter 1.perliminaries
1.1 probability
1.2 random variables
1.3 expected value
1.4 moment generating , characteristic functions,and laplace transforms
1.5 conditional expectation
1.6 the exponential distribution,lack of memory,and hazard rate functions
1.7 some probability inequalities
1.8 limit theorems
1.9 stochastic processes
chapter 2.the poisson process
2.1 the poisson process
2.2 interarrival and waiting time distributions
2.3 conditional distribution of the arrival times
2.4 nonhomogeneous poisson process
2.5 compound poisson random variables and processes
2.6 conditional poisson processes
chapter 3.renewal theory
3.1 introduction and preliminaries
3.2 distribution of N(t)
3.3 some limit theorems
3.4 the key renewal theorem and applications
3.5 delayed renewal processes
3.6 renewal reward processes
3.7 regenerative processes
3.8 stationary point processes
chapter 4.markov chains
4.1 introduction and examples
4.2 chapman-kolmogorov equations and classification of states
4.3 limit theorems
4.4 transitions among classes the gambler`s ruin problem,and mean times in transient states
4.5 branching processes
4.6 applications of markov chains
4.7 time-reversible markov chains
4.8 semi-markov processes
chapter 5. continuous-time markov chains
5.1 introduction
5.2 continuous- time markov chains
5.3 birth and death processes
5.4 the kolmogorov differential equations
5.5 limiting probabilities
5.6 eime reversibility
5.7 applications of reversed chain to queueing
5.8 uniformization
chapter 6.martingales
6.1 martingales
6.2 stopping times
6.3 azuma`s inequality for martingales
6.4 submartingales,supermartingales,and the martingalb convergence theorem
6.5 a generalized azuma inequality
chapter 7. random walks
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