Momentum-space approach to asymptotic expansion for stochastic filtering

Masaaki Fujii ()

Annals of the Institute of Statistical Mathematics, 2014, vol. 66, issue 1, 93-120

Abstract: This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distribution. Thanks to the simplicity of the ODE system, higher-order calculation can be performed easily. Furthermore, solving ODEs sequentially with small sub-periods with updated initial conditions makes it possible to implement a substepping method for asymptotic expansion in a numerically efficient way. This is found to improve the performance significantly where otherwise the approximation fails badly. The method is expected to provide a useful tool for more realistic financial modeling with unobserved parameters and also for problems involving nonlinear measure-valued processes. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Keywords: Zakai equation; Polynomial-function approximation; Measure-valued process (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10463-013-0405-1

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