  For rare events described in terms of Markov processes, truly unbiased
estimation of the rare event probability generally requires the avoidance of
numerical approximations of the Markov process. Recent work in the exact and
$\varepsilon$-strong simulation of diffusions, which can be used to almost
surely constrain sample paths to a given tolerance, suggests one way to do
this. We specify how such algorithms can be combined with the classical
multilevel splitting method for rare event simulation. This provides unbiased
estimations of the probability in question. We discuss the practical
feasibility of the algorithm with reference to existing $\varepsilon$-strong
methods and provide proof-of-concept numerical examples.
