# Francois Le Gland

## Adapting the number of particles in sequential Monte Carlo methods

The original motivation for this problem is the approximation of unnormalized Feynman-Kac distributions and their normalizing constants, in the special case where the selection functions are only nonnegative and can take the zero value. Several important practical situations are described where this case occurs. If the selection functions are only nonnegative, it can happen with a standard particle algorithm that all the simulated particles receive a zero weight, with the effect that the particle system dies out. To guarantee that the particle system never dies, a sequential particle algorithm is introduced, which adapts the number of particles, and some limit theorems are proved, including a central limit theorem. While in standard particle algorithms the computational effort is fixed but the performance cannot be guaranteed, in the proposed sequential particle algorithm the performance is guaranteed at the expense of a random computational effort. Intuitively speaking, the number of particles is chosen large when the normalizing constant is small. The different results are illustrated in the simple case of binary selection functions. This is joint work with Nadia Oudjane (EDF RD and Université Paris XIII).