Section: New Results

Adaptive multilevel splitting

Participants : Frédéric Cérou, Arnaud Guyader.

We have show last year that an adaptive version of multilevel splitting for rare events is strongly consistent and that the estimates satisfy a CLT (central limit theorem), with the same asymptotic variance as the non–adaptive algorithm with the optimal choice of the parameters. This year we have generalized these results to include Markov kernels used to move the particles (or shakers) are of Metropolis–Hastings type. This is a non–trivial generalization to a very important case.