The <transition probability matrix> has entries
$$
P_{rs}(u)=\mathbb P(X(t+u)=s\mid X(t)=r)
$$
under the <time-homogeneous Markov property>. For the finite-state model in part d, the <transition semigroup of a continuous-time Markov chain> is
$$
P(u)=e^{uQ}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 1 / f / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-207/1/f/i/solution