Exponential stability for nonlinear filtering

Atar, Rami; Zeitouni, Ofer

doi:10.1016/s0246-0203(97)80110-0

Cited by 101 publications

(110 citation statements)

References 18 publications

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“…The above result is generally proved for the filtering distribution (see e.g. [1], [7] and [11]). To prove it for the predictive distributions, we follow the scheme of [11].…”

Section: Tightness Of the Asymptotic Variancesmentioning

confidence: 69%

“…Assumption (A2), which is the most stringent, is nevertheless classical and is verified when X is compact. (see [1] and the chronological discussion in [11]). Assumptions (B1)-(B2) are mild.…”

Section: Notations Assumptions and Preliminary Resultsmentioning

confidence: 99%

“…Assume that b and σ lead to a strictly elliptic generator on M , with heat kernel G t (x, y). We refer to [1] and [5] for the following inequality…”

Section: The Case Of a Diffusion On A Compact Manifoldmentioning

confidence: 99%

“…Nevertheless, such an assumption is of common use in this kind of studies (see e.g. [1], [10]). In the sense of [10], it means that the whole state space of the hidden chain is "small" (see [10]).…”

Section: Introductionmentioning

confidence: 99%

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On the asymptotic variance in the central limit theorem for particle filters

Favetto

2012

ESAIM: PS

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Abstract.Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends on the set of observations. In this paper we establish, under general assumptions on the hidden Markov model, the tightness of the sequence of asymptotic variances when considered as functions of the random observations as the number of observations tends to infinity. We discuss our assumptions on examples and provide numerical simulations.Mathematics Subject Classification. 60G35, 62M20, 60F05, 60J05.

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“…The above result is generally proved for the filtering distribution (see e.g. [1], [7] and [11]). To prove it for the predictive distributions, we follow the scheme of [11].…”

Section: Tightness Of the Asymptotic Variancesmentioning

confidence: 69%

Section: Notations Assumptions and Preliminary Resultsmentioning

confidence: 99%

“…Assume that b and σ lead to a strictly elliptic generator on M , with heat kernel G t (x, y). We refer to [1] and [5] for the following inequality…”

Section: The Case Of a Diffusion On A Compact Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the asymptotic variance in the central limit theorem for particle filters

Favetto

2012

ESAIM: PS

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“…(See e.g. [3], [6], [38], [2].) We will not discuss this problem further in this paper; we only want to mention that the inequality proved in Section 12 (see Theorem 12.1) is similar to inequalities used in the literature, when proving the filter stability property for filtering processes.…”

Section: Introductionmentioning

confidence: 99%

On convergence in distribution of the Markov chain generated by the filter kernel induced by a fully dominated Hidden Markov Model

Kaijser

2016

Dissertationes Math.

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Consider a filtering process associated to a hidden Markov model with densities for which both the state space and the observation space are complete, separable, metric spaces. If the underlying, hidden Markov chain is strongly ergodic and the filtering process fulfills a certain coupling condition we prove that, in the limit, the distribution of the filtering process is independent of the initial distribution of the hidden Markov chain. If furthermore the hidden Markov chain is uniformly ergodic, then we prove that the filtering process converges in distribution.

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On the statistical analysis of quantized Gaussian AR(1) processes

Rásonyi

2009

Adaptive Control & Signal

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Exponential stability for nonlinear filtering

Cited by 101 publications

References 18 publications

On the asymptotic variance in the central limit theorem for particle filters

On the asymptotic variance in the central limit theorem for particle filters

On convergence in distribution of the Markov chain generated by the filter kernel induced by a fully dominated Hidden Markov Model

On the statistical analysis of quantized Gaussian AR(1) processes

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