What condition on the probability distribution is necessary and sufficient in order that a limiting distribution exist, and what is this limiting distribution?

The Markov chain is a description of the sequence of possible events in which the probability of an event depends only on the state attained in a previous separate event.

Step-by-step explanation:

The relation described by the Markov chain satisfies the following conditions:

1. All states communicate with themselves, that is P₁₁⁰ = 1 ≥ 0

2. There must be symmetry: if i←→j, then j ←→i

3. There must be transitivity. That is if i ←→k and k←→j, then i←→j

The conditions above imply that the communication is an example of an equivalence relation, meaning that it shares the properties with the more familiar relation, that is

i = i, if i = j, then j = i etc