I am aware of the existence of the following questions: How to discretely stochastically simulate a continuous-time Markov chain? Recipe to discretize a continuous- time markov process
I tried to understand them, but frankly, I couldn't.
Like in discreet time Markov chain, I want to find the probability of being in state $j$ at interval $k$ (discretized). I know of the rate matrix and initial probability distribution. How would I do that?
References will be appreciated.