Strong convergence of truncated implicit Euler-Maruyama algorithms for the Wonham filters

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Ma, Xiaohang and Mao, Xuerong and Wang, Le Yi and Yin, George (2025) Strong convergence of truncated implicit Euler-Maruyama algorithms for the Wonham filters. Mathematical Control and Related Files. ISSN 2156-8499 (https://doi.org/10.3934/mcrf.2025047)

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Abstract

This paper develops new numerical algorithms of Wonham filters for state estimation of hidden continuous-time Markov chains. Implementation of numerical solutions using Wonham filters encounters issues of algorithm stability and convergence. This paper introduces new algorithms that employ a truncated implicit Euler-Maruyama type of schemes to approximate Wonham filters. A logarithm transformation is used and then a truncation scheme is proposed to overcome the nonlinear growth of the coefficients and establish the strong convergence in the sense of Lp -convergence. Furthermore, a backward updating framework that enforces moment bounds on the log-posterior probability is suggested.

ORCID iDs

Ma, Xiaohang, Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864, Wang, Le Yi and Yin, George;
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