Hi,

I was hoping someone could help me with this question. I am having trouble understanding the generator matrix Q, so this whole question is difficult for me

.

Let $\displaystyle X = (X_t)$ be a Markov process with state space $\displaystyle \{1,2,3\}$ and generator

$\displaystyle Q = \begin{pmatrix} -3 & 2 & 1 \\ 2 & -5 & 3 \\ 1 & 3 & -4 \end{pmatrix}$

(1) Determine the sojourn times in 1,2 and 3

(2) Let $\displaystyle Y = \{Y_n\}$ be a discrete skeleton of $\displaystyle X$. Determine the stationary distribution $\displaystyle \nu$ of $\displaystyle Y$.

(3) Determine the stationary distribution $\displaystyle \pi$ of $\displaystyle X$.

Thanks in advance for any help.