Rare event simulation using reversible shaking transformations

We introduce random transformations, called reversible shaking transformations, which we use to design two schemes for estimating rare event probabilities. One is based on interacting particle systems and the other on the time-average of a single Markov path (called POP for parallel one-path) using ergodic theorem. We discuss their convergence rates and provide numerical experiments including continuous stochastic processes and jump processes. Our examples cover important situations related to insurance, queueing systems, and random graphs. Both schemes have good performance, with a seemingly better one for POP.