6 problems

Variance bound conjecture. The variance of the estimator is upper-bounded by an expression of order

Let $\rho_n^m$ be the particle approximation at iteration $n$ with $m$ particles, let $\rho^*$ be the target measure, and let $\tilde{\rho}_\tau^*$ be a good approximation of…

Let $\rho_n^m$ be the particle approximation produced at iteration $n$ with $m$ particles, let $\rho^*$ be the target measure, and let $\tilde{\rho}_\tau^*$ be a numerical referenc…

Let an SMC algorithm use a stochastic rounding resampling scheme satisfying the standing assumption, and suppose that the incremental transition densities $g_t(x,x')$ satisfy … for…

Let $(E,\mathcal{E})$ be the state space, let $\mu$ be the initial distribution, and let $\pi$ be the target invariant distribution. For each $n$ and $0\leq k\leq n$, let…

The particle method uses an entropy fix: a merge is rejected a posteriori when the shock-resolution condition is not satisfied, after which points are inserted near the shock and t…