Abstract
In this paper, we present a reliable method that can be used to sample paths of a diffusion process described by a system of stochastic differential equations. These are types of processes whose transition density is not known in closed form. This reliable method involves solving a partial differential equation of the Fokker-Planck type by rejection sampling techniques applied to the associated densities. We then use the novel method to sample from the Ornstein-Uhlenbeck (OU) process whose transition density is known and has unbounded drift. The results obtained compare excellently with the analytical results, thus rendering the method reliable and accurate. The method is then used to sample from diffusions whose transition densities are unknown in closed form. This work has its applications in population genetics; accordingly, we sample paths of theWright-Fisher diffusions that have a bounded drift.
Recommended Citation
Kikabi, Yasin and Kasozi, Juma
(2024).
(R2072) A Method to Sample from Transition Densities of Diffusion Processes with Unknown Densities,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 21,
Iss.
1, Article 1.
Available at:
https://digitalcommons.pvamu.edu/aam/vol21/iss1/1