Let X be a birth- and death-process with and with birth intensity φ and death intensity µ, that is, Let Nb(t) and Nd(t) be the number of births and deaths, respectively, in [0,t]. (A transition...

Let X be a birth- and death-process with

and with birth intensity φ and death intensity µ, that is,

Let N_b(t) and N_d(t) be the number of births and deaths, respectively, in [0,t]. (A transition from state j to state j +1 is a birth, while a transition from state j to state j−1 is a death.) Use (1.11) to determine the intensity processes of the two counting processes.