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We establish the convergences (with respect to the simulation time $t$; thenumber of particles $N$; the timestep $\gamma$) of a Moran/Fleming-Viot typeparticle scheme toward the quasi-stationary distribution of a diffusion on the$d$-dimensional torus, killed at a smooth rate. In these conditions,quantitative bounds are obtained that, for each parameter ($t\rightarrow\infty$, $N\rightarrow \infty$ or $\gamma\rightarrow 0$) are independent fromthe two others.

Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: uniform estimates in a compact soft case