Stability of nonlinear filters in nonmixing case

By P. Chigansky, Robert Sh. Liptser. 2003

48 citations recorded by the source corpus.

The nonlinear filtering equation is said to be stable if it ``forgets'' the initial condition. It is known that the filter might be unstable even if the signal is an ergodic Markov chain. In general, the filtering stability requires stronger signal ergodicity provided by the, so called, mixing condition. The latter is formulated in terms of the transition probability density of the signal. The most restrictive requirement of the mixing condition is the uniform positiveness of this density. We show that it might be relaxed regardless of an observation process structure.

Subfields: Artificial Intelligence, Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0e71cec5b68d8cfb44f3c4d360199b3778fa32fe

How researchers see this paper

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In Artificial Intelligence

1. Pierre-Francois Marteau
2. Valérie Monbet
3. Pierre Ailliot

In Statistics and Probability

1. Valérie Monbet
2. Pierre Ailliot

Citations in the corpus

• L1-convergence of smoothing densities in non-parametric state space models (2008, background): “It is an usual assumptions to get the contractivity of the forward operator (see [3] and [7]), but several authors have recently proposed to refine it (see [6] and references therein).”