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

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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https://hal.univ-cotedazur.fr/hal-01301157
Contributor : Sylvain Rubenthaler <>
Submitted on : Monday, January 27, 2020 - 3:01:07 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:53 PM
Document(s) archivé(s) le : Tuesday, April 28, 2020 - 12:06:38 PM

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  • HAL Id : hal-01301157, version 3
  • ARXIV : 1604.03345

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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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