An inverse problem in birth and death processes

Abstract

AbstractAn inverse problem of constructing birth and death processes X(t)⊮n finite state space 0, 1, 2, …, N n0 ⊮s considered. Given a set of 2N + 1, distinct, nonnegative real numbers one of which is zero, say 0 = s0 < z1 < 2< … < zN < sN,a procedure is established to obtain the birth and death rates of a birth and death process so that P(X(t)=0)=∑j=0NΠi=1N(zi −sjΠi=0,iǂjN(si − sje−sjtother transient system size probabilities. This technique is illustrated numerically