  For a class of partially observed diffusions, conditions are given for the
map from the initial condition of the signal to filtering distribution to be
contractive with respect to Wasserstein distances, with rate which does not
necessarily depend on the dimension of the state-space. The main assumptions
are that the signal has affine drift and constant diffusion coefficient and
that the likelihood functions are log-concave. Ergodic and nonergodic signals
are handled in a single framework. Examples include linear-Gaussian, stochastic
volatility, neural spike-train and dynamic generalized linear models. For these
examples filter stability can be established without any assumptions on the
observations.
