I have a continuous-time markov process and I need to calculate the following:
- transition frequencies matrix (aka intensity matrix)
- transition probabilities
- all parameters which define permanence times in states
- the transition frequencies diagram
- the balance equations for the probability flux while in transient
- the markov discrete-time chain stochastically undistinguishable
Here's what I did:
I wrote the matrix (first point) since it's an easy one.
$P(X(1)=j|X(0)=i) = \frac{q_{i,j}}{v_i}$
I think the parameters is here referring are the $\pi_i$ stationary probabilities since Permanence_time = $\pi_i*h$ where h is the time interval
this should be the graphical representation with nodes and arcs from the first point's matrix, and I did this without problems
I don't know what this point is referring to
Idem, I don't know what does that mean
Can someone shed a bit of light on the last two points? I don't want the exercise done without trying, but I don't know how to proceed