  We propose a general method to obtain approximation of the first passage time
distribution for the birth-death processes. We rely on the general properties
of birth-death processes, Keilson's theorem and the concept of Riemann sum to
obtain closed-form expressions. We apply the method to the three selected
birth-death processes and the sophisticated order-book model exhibiting
long-range memory. We discuss how our approach contributes to the competition
between spurious and true long-range memory models.
