A new rejection sampling method without using hat function (Q2405113)

This paper presents a new exact simulation method which simulates a realisation of a given density of a distribution \(f\). The main benefit of the proposed techique is that -- as opposed to existing techniques -- no hat function is required to bound \(f\). The method is based on running two independent diffusion processes where the product of the invariant distributions of the two diffusions equals \(f\). Rejection sampling is used to determine the time point at which the two independent processes coalesce. The paper generalises this technique for distributions that can be decomposed into arbitrarily many distributions using layered Brownian motion. Simulation results show an empirical validation of the proposed technique.