Dimension-free Wasserstein contraction of nonlinear filters

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