No abstract

This paper studies Galerkin approximations applied to the Zakai equation of stochastic filtering. The basic idea of this approach is to project the infinite-dimensional Zakai equation onto some finite-dimensional subspace generated by smooth basis functions; this leads to a finitedimensional system of stochastic differential equations that can be solved numerically. The contribution of the paper is twofold. On the theoretical side, existing convergence results are extended to filtering models with observations of point-process or mixed type. On the applied side, various issues related to the numerical implementation of the method are considered; in particular, we propose to work with a subspace that is constructed from a basis of Hermite polynomials. The paper closes with a numerical case study.

HSE, etc. His extensive publications include over 60 refereed journal papers and two research books. Professor Wang's major research interests include safety and reliability based design and operations of large marine and offshore systems. Dr Ling Xu is a research fellow in the Manchester Business School, working in the areas of decision analysis, decision support, and decision technology. As a co-designer, she developed two window based assessment tools called IDS Multi-Criteria Assessor and IDS Cost Estimator, and several web based assessment and decision support tools. Dr Xu has published a G

We give a correction to Theorem 1.2 in a previous paper [Mediterr. J. Math. (2018) 15:227]. Two examples are given to explain the corrected conclusion.

No abstract