Hey rhet, I was woundering if you could give me a little help with a problem im trying to solve. Im doing an actuarial module and one of the things we study is continuous time markhov chain processes. Obviously being an actuarial module we apply it to life insurance, but I thought i'd take a break from it and try apply it to something which is very important to all of us, coldsnaps total. I'm modeling it as having 3 states, 800a, 900b and 1000c. Here is the diagram with the states and the relevant intensities.
Trying to work out what the forward equation P(b,c)[t,u] is. t is current time, u is a future time, which for our case could be january first 2015. This would be very simple if the intensities y2 and z2 didn't exist because then this would be just like an active, inactive, dead markhov chain, but coldsnaps total has gone from 1000 back down to 900 so it wouldn't be realistic.
Would it be
obvs all intensities are functions of time. Obviously this is not the most realistic model because his total can take any value making Z infinite, but fuck that, 3 states was hard enough to think about.