Summary
This chapter is an introduction to the theoretical study of particle estimates: how they converge as N → +∞, and whether their error stays stable over time. The focus is on results that are easy to prove from first principles. References to more technical results are given in the bibliography at the end of the chapter.
A key idea is that the error of a particle estimate at time t may be decomposed into a sum of ‘local’ errors that correspond to the previous time steps 0, 1, …, t. In that spirit, most proofs will rely on an induction argument.
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Chopin, N., Papaspiliopoulos, O. (2020). Convergence and Stability of Particle Filters. In: An Introduction to Sequential Monte Carlo. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-47845-2_11
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