Beskos, Alexandros; Crisan, Dan O.; Jasra, Ajay; Whiteley, Nick Error bounds and normalising constants for sequential Monte Carlo samplers in high dimensions. (English) Zbl 1291.65009 Adv. Appl. Probab. 46, No. 1, 279-306 (2014). Sequential Monte Carlo (SMC) samplers are considered which simulate a collection of \(N\) weighted samples in parallel. These samples (particles) are propagated in time via MCMC with importance sampling to derive a sample from a target density in \(\mathbb R^d\). The authors derive estimates for \(L_2\)-error of SMC as \(d\to\infty\) when \(N\) is fixed. (In fact the target densities considered are densities of random vectors with i.i.d. entries).In the case when resampling is done at the very final time step it is shown that \(L_2\)-error increases by a factor of \(O(N^{-1})\) uniformly in \(d\). Estimation of a ratio of normalizing constants and asymptotic independence properties of the particles are also addressed. Reviewer: R. E. 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