Title: Dimension-free Wasserstein contraction of nonlinear filters,
Abstract: For a class of partially observed diffusions, sufficient conditions are given
for the map from initial condition of the signal to filtering distribution to
be contractive with respect to Wasserstein distances, with rate which has no
dependence on the dimension of the state-space and is stable under tensor
products of the model. The main assumptions are that the signal has affine
drift and constant diffusion coefficient, and that the likelihood functions are
log-concave. Contraction estimates are obtained from an $h$-process
representation of the transition probabilities of the signal reweighted so as
to condition on the observations.