QBank: 5.11 ii

Question: In a three state Markov model, prove that:

d/dt t_P_x (HH bar) = - t_P_x(HH bar) {sigma_x+t + mu_x+t}


I begin this with:

t+h_P_x (HH bar) = 1 - t+h_P_x (HS) - t+h_P_x (HD)

then is the usual

P (HS) = P (HH).P (HS) + P(HH).P (HD) + P (HS).P(SS)

substituting all the h_P_x+t (Hk) with {h.force + o(h)}

This won't work because of the red term, but why?

 

tPx HH bar is the one where you stay in healthy for the whole time - not just start and end there so you cant go via other states.

Do t+hPx = tPx * t+hPx+t

then t+hPx+t is h*(negative sum of forces leaving state H)

then follow all the other steps you should be familiar with.

 

thanks geoff

will remember that next time.