2. Stochastic Processes

Markov Processes — Quiz

Test your understanding of markov processes with 5 practice questions.

Read the lesson first

Practice Questions

Question 1

Which of the following defines the transition semigroup $\{P(t)\}_{t\ge0}$ for a continuous-time Markov process?

Question 2

For a continuous-time Markov chain with generator $Q$ and semigroup $P(t)=e^{tQ}$, which differential equation holds?

Question 3

Given a two-state generator $Q=\begin{pmatrix}-\lambda & \lambda\\mu & -\mu\end{pmatrix}$, what is the transition probability $P_{01}(t)$?

Question 4

Which constraints must the transition rates $q_{ij}$ of a CTMC satisfy for all $i\neq j$?

Question 5

In a discrete-time credit rating model with states {A,B,D} and transition matrix $\begin{pmatrix}0.8&0.15&0.05\\0&0.9&0.1\\0&0&1\end{pmatrix}$, what is the probability of default within two steps starting from A?