Non-linear filtering using random particles

This paper is concerned with extending the particle solution of nonlinear discrete-time filtering problems developed in [Ph.D. thesis, Universitй Paul Sabatier, Tolouse, France, 1994], [Contrat 89.34.553.00.470.75.01, DIGILOG-DRET, 1992], and [Proc. l4iйme Colloque GRETSI, Juan les Pins, September, 13–16, 1993] to continuous-time problems. The minimal sufficient conditions for a time-uniform convergence of our particle filter are quite similar to those described in [Ph.D. thesis, Universitй Paul Sabatier, Tolouse, France, 1994]. Guided by Sussmann's condition, which ensures the continuity of the conditional expectation, we introduce a new regularity concept in this paper.