General Birth and Death Process

• Consider (Feller, p. 404) a system with a denumerable number of states whose probability of occupation varies with t.

• For Poisson is ``we have observed n events.''

  Note only one occupied at a time

  and chance of a transition .

  This is a pure birth process.

• We can generalize to : a function of n and t.

• Also, we can have death processes which also allow relapses to with chance . So:

  

• We can, at once, derive a similar differential equation for : the probability of system being in state .

  

• with and so that above is still correct with n=0.