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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

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