The Mean of Birth-Death Processes

Abstract

Consider a natural birth-death process {X(t): 0 ≤ t < ∞} with µ₀ = 0 and let m(t) denote the first moment of X(t), i.e.,

$$ m(t) = \sum\limits_{j = 0}^\infty{j{P_j}(t).} $$

((9.1.1))