L^p(p > 1) convergence results for particle filtering

In this paper, we prove Lp-convergence for p > 1 of the particle filter for a class of unbounded functions. Furthermore, it can be shown that the approximation solution converges in probability to the true optimal estimate for the case 1 < p ≤ 2 and the approximation solution converges almost surely to the true optimal estimate for the case p > 2. In addition, some numerical experiments are presented to illustrate the main convergence results.