Stochastic Processes · 免费预览
连续时间链的定义
连续时间链在实时间上保持马尔可夫性质，由从 i 到 j 的跳转速率 q 描述，而非一步转移概率；其构造方式是先在每个状态按总退出速率停留一个指数时间，再依据离散时间的转移路线图进行转移。
1. The Markov property on a continuous clock
The Markov property on a continuous clock
2. Reading a rate diagram
Reading a rate diagram
3. Building the chain from a roadmap
Building the chain from a roadmap
4. Uniformizing the clock
Uniformizing the clock
5. The defining property
What does the Markov property say for a continuous-time chain?
6. What a jump rate is
How is the jump rate q of i comma j defined for j different from i?
7. Adding up the exits
A state i has jump rates 2 to state a and 3 to state b, and no other exits. What are the total exit rate and the mean holding time?
8. Routing the departure stream
With jump rates 2 to a and 3 to b out of state i, what is the probability that the chain moves to a when it leaves?
9. Constructing from a roadmap
How does the formal construction turn rates into a process?
10. When chains explode
The pure birth process has jump rate i to the power p from state i to state i plus one. When does it explode?
11. A state's total drain
From a certain state, a chain jumps to state a at rate 2 and to state b at rate 3, with no other moves possible. Compute the total exit rate from the state and write the number.
12. Where the departure goes
With the same exit rates, 2 toward a and 3 toward b, compute the routing probability of moving to a when the chain leaves, and write the answer as a fraction or decimal.
13. The first hold in a pure birth
A pure birth process moves from state 3 to state 4 at rate 3 squared, that is 9. Compute the mean holding time in state 3 and write the answer as a fraction or decimal.