Large deviations for additive path functionals and convergence properties for numerical approaches based on population dynamics have attracted recent research interest. The aim of this paper is twofold. Extending results from the literature of particle filters and sequential Monte Carlo methods we can establish rigorous bounds on convergence properties of the cloning algorithm in continuous time, which are reported in this paper with details of proofs given in a further publication. Secondly, the tilted generator characterizing the large deviation rate function can be associated to non-linear processes which give rise to several representations of the dynamics and additional freedom for associated particle approximations. We discuss these choices in detail, and combine insights from the filtering literature and the cloning algorithm to suggest a more efficient version of the algorithm.
Angeli, Letizia; Grosskinsky, Stefan; Johansen, Adam M.; Pizzoferrato, Andrea. (2018). Rare event simulation for stochastic dynamics in continuous time. arXiv:1810.00693.