Stationary probabilities of markov chain

Question

I am confused in which conditions the stationary probabilities of both discrete and continuous Markov chain donot exist.

If it is due to periodic chain then is it for both discrete and continuous.

and one thing more the sum of row of the transition matrix of both discrete or continuous both is 1 or only discrete.

Answer 1

In a continuous MC values in the $Q$ matrix are rates: usually $\lambda$ for going to the next state, $\mu$ to the previous state, and the diagonal value is $-(\lambda+ \mu)$, so they sum to 0.

From this you can obtain a jump matrix by standardizing: divide every row by $\lambda +\mu$ and set the diagonal value to 0 (hence 'jump'). Then row values will sum to 1.