Markov chains: positive recurrence

Dependencies:

1. Markov chain
2. Markov chains: recurrent states

$\newcommand{\E}{\operatorname{E}}$ Let $X = [X_0, X_1, \ldots]$ be a markov chain. Let $i$ be a recurrent state. Let $T_i = \min_{t \ge 1} (X_t = i)$. Then $i$ is called positive recurrent iff $\E(T_i \mid X_0 = i)$ is finite. Otherwise, $i$ is called null recurrent.

Dependency for:

1. Markov chains: positive recurrence is a class property
2. Markov chains: finite sink is positive recurrent

Info:

• Depth: 8
• Number of transitive dependencies: 19

Transitive dependencies:

1. /sets-and-relations/de-morgan-laws
2. /sets-and-relations/countable-set
3. /analysis/topological-space
4. Group
5. Ring
6. Semiring
7. Matrix
8. σ-algebra
9. σ-algebra is closed under countable intersections
10. Measure
11. Probability
12. Conditional probability (incomplete)
13. Generated σ-algebra
14. Measurable function
15. Borel algebra
16. Generators of the real Borel algebra (incomplete)
17. Random variable
18. Markov chain
19. Markov chains: recurrent states