A Moran particle system approximation of Feynman-Kac formulae

We present a weighted sampling Moran particle system model for the numerical solving of a class of Feynman-Kac formulae which arise in different fields. Our major motivation was from nonlinear filtering, but our approach is context free. We will show that under certain regularity conditions the resulting interacting particle scheme converges to the considered nonlinear equations. In the setting of nonlinear filtering, the -convergence exponent resulting from our proof also improves recent results on other particle interpretations of these equations.