Introduction

This Julia and Maple code accompanies the research article "Numerical evaluation of the transition probability of the simple birth-and-death process" by Pessia A. and Tang J. (2019). A pre-print version of the article can be found on arXiv.

Setup

First of all, you obviously need a working Julia installation. Download and install the latest stable version from the official Julia website.

You now need to install package SimpleBirthDeathProcess and third-party packages KahanSummation, SpecialFunctions, and Plots. Use the following commands in a Julia environment to install all required packages:

• Enter the Pkg mode by pressing ]
• Issue the command add KahanSummation SpecialFunctions Plots
• Issue the command add https://github.com/albertopessia/SimpleBirthDeathProcess.jl
• Press the Backspace key to return to the normal Julia prompt

How to use the code

To generate numerically accurate values in arbitrary precision you need a working installation of Maple 2018. Simply issue the command read "log_trans_prob.mpl".

Figures 1, 3, and 4 can be recreated by copy/pasting the corresponding source code. Published figures were edited and finalized with Inkscape.

Values in Tables 1-4 can be obtained by using code found in Tables.jl. Note that this particular operation requires very long computation times and should only be tried in parallel on cluster servers.