Simulating branching processes via size constrained systems
Branching processes arise naturally in the study of fissile systems. In a wide variety of situations, it can be shown that these systems exhibit a Perron Frobenius type behaviour, that is, when normalised by the average growth of the system, the first moment of the branching process converges to a stationary distribution. Thus, efficiently estimating the growth rate and stationary distribution is imperative to understanding the leading order behaviour of the underlying fission process.
Recently, Cox, Horton and Villemonais have developed a resampling and selection model  that allows one to simulate branching processes and estimate such quantities, while keeping control over the population size. Roughly speaking, particles evolve according to a branching process until either the number of particles becomes too high or too low, in which case particles are either removed (selection) from the system or duplicated (resampling), respectively.
As a result of this research, many open questions have arisen, including extending this model to more general branching systems, understanding the effects of different resampling and selection mechanisms, stability analysis of the system and variance reduction techniques to name a few.
 Cox, A. M., Horton, E., & Villemonais, D. (2022). Binary branching processes with Moran type interactions. arXiv preprint arXiv:2207.03323.