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On the two-filter approximations of marginal smoothing distributions in general state space models

Abstract : A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state given future observations.
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Submitted on : Friday, May 27, 2016 - 12:07:30 AM
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Thi Ngoc Minh Nguyen, Sylvain Le Corff, Éric Moulines. On the two-filter approximations of marginal smoothing distributions in general state space models. Advances in Applied Probability, Applied Probability Trust, 2018, 50 (1), pp.154-177. ⟨10.1017/apr.2018.8⟩. ⟨hal-01319747⟩

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