Quotation Frey, Rüdiger, Schmidt, Thorsten, Xu, Ling. 2013. On Galerkin Approximations for the Zakai Equation with Diffusive and Point Process Observations. SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics) 51 (4): 2036-2062.


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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 finite-dimensional 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 working with a subspace that is constructed from a basis of Hermite polynomials. The paper closes with a numerical case study.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics)
Citation Index SCI
WU-Journal-Rating new FIN-A
Language English
Title On Galerkin Approximations for the Zakai Equation with Diffusive and Point Process Observations
Volume 51
Number 4
Year 2013
Page from 2036
Page to 2062
URL http://epubs.siam.org/doi/abs/10.1137/110837395

Associations

People
Frey, Rüdiger (Details)
External
Schmidt, Thorsten
Xu, Ling
Organization
Institute for Statistics and Mathematics IN (Details)
Institute for Finance, Banking and Insurance IN (Details)
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