STABILITY OF THE OPTIMAL FILTER IN CONTINUOUS TIME: BEYOND THE BENEŠ FILTER - Université Côte d'Azur Access content directly
Preprints, Working Papers, ... Year : 2016

STABILITY OF THE OPTIMAL FILTER IN CONTINUOUS TIME: BEYOND THE BENEŠ FILTER

van Bien Bui
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Sylvain Rubenthaler

Abstract

We are interested in the optimal filter in a continuous time setting. We want to show that the optimal filter is stable with respect to its initial condition. We reduce the problem to a discrete time setting and apply truncation techniques coming from [OR05]. Due to the continuous time setting, we need a new technique to solve the problem. In the end, we show that the forgetting rate is at least a power of the time t. The results can be re-used to prove the stability in time of a numerical approximation of the optimal filter.
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Dates and versions

hal-01301157 , version 1 (11-04-2016)
hal-01301157 , version 2 (18-10-2016)
hal-01301157 , version 3 (27-01-2020)

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van Bien Bui, Sylvain Rubenthaler. STABILITY OF THE OPTIMAL FILTER IN CONTINUOUS TIME: BEYOND THE BENEŠ FILTER. 2016. ⟨hal-01301157v3⟩
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