Stability and Uniform Particle Approximation of Nonlinear Filters in Case of Non Ergodic Signals

By N. Oudjane, Sylvain Rubenthaler. 2005

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Stability of nonlinear filters in nonmixing case (2003, background): “For instance, in order to have (1.3), (x,y) is required to be compactly supported (see [4]), or to have tails with certain decay rate depending on the signal model (see [1, 5, 9, 10, 16 ]).”
Uniform time average consistency of Monte Carlo particle filters (2008, methodology): “Though various methods have been proposed to extend the class of models to which the mixing assumption is applicable, essentially all subsequent work on uniform convergence of the particle filter [18, 19, 24, 16, 23, 22] has ultimately relied on a form of this strong assumption.”
SMC2: an efficient algorithm for sequential analysis of state space models (2011, background): “This is due to both high dependence between parameters and the latent process, which affects Gibbs sampling strategies (Papaspiliopoulos et al., 2007), and the difficulty in designing efficient simulation schemes for sampling from πT (x0:T |θ).”