A NOTE ON THE INTEGRAL FOR BIRTH-DEATH MARKOV PROCESSES

Let X(t) be a birth-death Markov process. Here it is shown how the expectation of the time to absorption and of the integral under X(t) up to absorption time can be found by substituting transitions to state 0 by transitions to the initial state of the process, provided the stationary distribution of the modified process exists. Examples of applications to some special cases of birth-death Markov processes are given. STOCHASTIC INTEGRALS; BIRTH AND DEATH PROCESS; MARKOV PROCESSES 1