  This paper addresses finite sample stability properties of sequential Monte
Carlo methods for approximating sequences of probability distributions. The
results presented herein are applicable in the scenario where the start and end
distributions in the sequence are fixed and the number of intermediate steps is
a parameter of the algorithm. Under assumptions which hold on non-compact
spaces, it is shown that the effect of the initial distribution decays
exponentially fast in the number of intermediate steps and the corresponding
stochastic error is stable in \mathbb{L}_{p} norm.
