Stochastic Processes · 免费预览
状态的分类
若链必然返回某状态，则该状态是常返的；若可能永不返回，则该状态是暂态的。每个有限链都可分解为暂态状态与由常返状态构成的闭合不可约类。
1. Will the chain come back
Will the chain come back
2. Communication and a transience test
Communication and a transience test
3. Closed sets and irreducible classes
Closed sets and irreducible classes
4. The decomposition of a finite chain
The decomposition of a finite chain
5. The dividing probability
Let T_y be the time of the first return to y and let rho of y, y be P_y(T_y finite). What distinguishes a recurrent state from a transient one?
6. Why absorbing states are recurrent
In the gambler's ruin chain, why is the absorbing fortune 0 a recurrent state?
7. Escape routes from an interior fortune
In the gambler's ruin chain on states 0 to 4 with win probability 0.4, starting from fortune 2, which computation shows state 2 is transient?
8. Transient states in the seven-state chain
In the seven-state chain of this lesson, which states are transient?
9. What closed means
In the seven-state chain, why is the set containing states 1 and 5 called closed?
10. A recurrent state's obligations
If state x is recurrent and x communicates with y, what must be true, and why?
11. An escape probability
In the gambler's ruin chain on states 0 to 4 with win probability 0.4, compute the probability, starting from fortune 2, of taking the route down to 1 and then down to 0, and write the number as a decimal.
12. Counting recurrent states
In the seven-state chain of this lesson, count the recurrent states and write the number.
13. Three returns to a transient state
A transient state y has return probability rho of y, y equal to 0.7. Compute the probability that the chain starting at y returns to y at least three times, and write the number as a decimal.