2013/11/22 by Paul A. Jenkins, Jenkins, Paul A. · 2 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #Statistical Methods and Bayesian Inference #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #stat.CO #stat.ME
paper · pdf · doi:10.48550/arxiv.1311.5777
19 pages, 1 figure
arxiv created 2013/11/22 · openalex publication_date 2013/11/22 · arxiv updated 2013/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.