Rare event simulation for stochastic dynamics in continuous time

TL;DR

This paper investigates the convergence properties of cloning algorithms in continuous-time stochastic dynamics, establishing rigorous bounds and connecting them to particle filtering methods to enhance numerical efficiency.

Contribution

It provides the first rigorous convergence bounds for cloning algorithms in continuous time and links these methods to particle filters for improved numerical approximation.

Findings

Established convergence bounds for cloning algorithms in continuous time

Connected cloning algorithms to particle filtering and sequential Monte Carlo methods

Discussed multiple representations of dynamics for numerical improvements

Abstract

Large deviations for additive path functionals of stochastic dynamics and related numerical approaches have attracted significant recent research interest. We focus on the question of convergence properties for cloning algorithms in continuous time, and establish connections to the literature of particle filters and sequential Monte Carlo methods. This enables us to derive rigorous convergence bounds for cloning algorithms which we report in this paper, with details of proofs given in a further publication. 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 numerical approximations. We discuss these choices in detail, and combine insights from the filtering literature and cloning algorithms to compare different approaches and improve efficiency.