This report contains supplementary material for the paper [1], and gives detailed proofs of all lemmas and theorems that could not be included into the paper due to space limitations. The notation is adapted from the paper.

[1] C. Fritsche, U. Orguner, and F. Gustafsson, “Bobrovsky-Zakai bound for filtering, prediction and smoothing ofnonlinear dynamic systems,” in International Conference on Information Fusion (FUSION), Cambridge, UK, Jul.2018, pp. 1–8.