Approximation of the first passage time distribution for the birth–death processes

Abstract

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.