Hello everyone,

For my research I currently have to deal with Master Equations stemming from Markov processes. I find this very interesting, but am currently facing a challenge. My project involvesba (fairly simple) Markov chain: an item starts in point 1 (call it healthy) and throughout time, it can either transition to a second point 2 (call it dead) with transition probability of x, or it will not switch. Items from state 2 remain in state 2, so what's dead stays dead.

I was able to set up a master equation for this, but would now like to distinguish three different cases. Assume there are two such items, each going through the exact same Markov chain. How do I set up a Master Equation for this if the two events are a) perfectly uncorrelated, b) perfectly correlated (positively or negatively), or c) (the most interesting case, of course) imperfectly correlated.

I have little experience with this, and I do not require anyone to give me a solution, but rather an idea on where to look, perhaps also under which keywords, to come up with the solution myself. I hope this was acceptable to post here, thank you!