# Tagged Questions

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### Continuous time markov chains, is this step by step example correct

I have some questions regarding CTMC... and most importantly whether the step-by-step example I provide below is correct. My main sources about CTMC are: ([1], and [2]). Let's assume 3 possible ...
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### Can the transition probabilities of an inhomogeneous Markov chain be written as an exponential?

If $Z_t$ is a homogeneous continuous-time Markov chain with finite state space $E=\{1,\ldots,p\}$, transition matrices $(P(t))$ and intensity matrix $Q$, it holds that $$P(t) = \exp(tQ),$$ see for ...
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### Board Game Markov Process - Transient Probabilities

I need to write an essay on the Game of Life board game, and so I studied up on Markov Chains to help me calculate the probabilities and average payoffs for the spaces; however I'm not sure whether ...
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### Q-matrix vs. P-matrix description of a Markov chain

Consider a continuous time Markov chain $(X_t)_{t \geq 0}$ on some state space $S$ with transition matrix (P-matrix) $p_t(x,y)$, the probability density of jumping from $x$ to $y$ in time $t$. The ...
Let us denote $f_j^{(n)}$ denote the probability of the first return to state $j$after n transitions. Let $p_{jj}^{(n)}$ be the probability of returning to the state $j$ after $n$ transitions when ...