Section: New Results

Convergence of a two–step multilevel splitting algorithm for rare event simulation

Participants : François Le Gland, Damien--Barthélémy Jacquemart.

The problem is to accurately estimate the (very small) probability that a rare but critical event (such as a score function exceeding a given threshold) occurs before some fixed final time. Multilevel splitting is a very efficient solution, in which sample paths are propagated and are eliminated or replicated when some intermediate events (defined by some intermediate thresholds) occur. A common and efficient design is to define the next intermediate level as an empirical quantile of the running maximum of the score function along a surviving trajectory. However, it is practically impossible to remember when (at which time instant) and where (in which state) did each successful trajectory cross the empirically defined threshold. The proposed design is a two–step adaptive multilevel splitting algorithm: In the first step, a first set of trajectories is sampled in order to obtain the next intermediate threshold as an empirical quantile. In the second step, once the new intermediate threshold is obtained, a second set of trajectories is sampled in order to evaluate the transition probability to the new empirically defined intermediate region. This two–step procedure is repeated until some trajectories do hit the critical region before final time.

This work has been presented at the 10th International Workshop on Rare Event Simulation (RESIM), held in Amsterdam in August 2014.