Stability of the optimal filter in continuous time: beyond the Beneš filter. Issue 5 (2nd September 2020)

• Record Type: Journal Article
• Authors: Bui, Van Bien; Rubenthaler, Sylvain
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 5(2020)
• Page Start: 797
• Page End: 855
• Publication Date: 2020-09-02
• Subjects: Filtering -- signal detection -- inference from stochastic processes; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1727345
• Languages: English
• ISSNs: 0736-2994

Abstract

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. 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.