Exact simulation of the sample paths of a diffusion with a finite entrance boundary

Diffusion processes arise in many fields, and so simulating the path of a diffusion is an important problem. It is usually necessary to make some sort of approximation via model-discretization, but a recently introduced class of algorithms, known as the exact algorithm and based on retrospective rejection sampling ideas, obviate the need for such discretization. In this paper I extend the exact algorithm to apply to a class of diffusions with a finite entrance boundary. The key innovation is that for these models the Bessel process is a more suitable candidate process than the more usually chosen Brownian motion. The algorithm is illustrated by an application to a general diffusion model of population growth, where it simulates paths efficiently, while previous algorithms are impracticable.