Accessible State
Jump to navigation
Jump to search
See: Markov Process State, Graph Path, Markov Chain, Recurrent State.
References
2011
- http://en.wikipedia.org/wiki/Markov_chain#Reducibility
- QUOTE: A state j is said to be accessible from a state i (written i → j) if a system started in state i has a non-zero probability of transitioning into state j at some point. Formally, state j is accessible from state i if there exists an integer n ≥ 0 such that [math]\displaystyle{ \Pr(X_{n}=j | X_0=i) = p_{ij}^{(n)} \gt 0.\, }[/math] Allowing n to be zero means that every state is defined to be accessible from itself.
2010
- (Riddles, 2010) ⇒ (2010). “Introduction to Stochastic Processes.
- QUOTE: Accessible: A state j is accessible from state i if there is a path from state i to state j. There is a path if pij(n) > 0 for some n > 0.
Recurrent States: State i is recurrent if for every state j that is accessible from state [math]\displaystyle{ i }[/math], state i is also accessible from state j.
- QUOTE: Accessible: A state j is accessible from state i if there is a path from state i to state j. There is a path if pij(n) > 0 for some n > 0.