Geometric Ergodicity and Wasserstein Continuity of Non-Linear Filters

Abstract: In this paper, we present conditions for the geometric ergodicity and Wasserstein regularity of non-linear filter processes. While previous studies have mainly focused on unique ergodicity and the weak Feller property, our work extends these findings in three directions: (i) We present conditions on the geometric ergodicity of non-linear filters, (ii) we obtain further conditions on unique ergodicity for the case where the state space is compact which complements prior work involving countable spaces, and (iii) as a by-product of our analysis, we obtain Wasserstein continuity of non-linear filters with stronger regularity.