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SEM modeling with singular moment matrices. II: ML-estimation of sampled stochastic differential equations. (English) Zbl 1275.60055

Summary: Linear stochastic differential equations are expressed as an exact discrete model (EDM) and estimated with structural equation models (SEMs) and the Kalman filter (KF) algorithm. The oversampling approach is introduced in order to formulate the EDM on a time grid which is finer than the sampling intervals. This leads to a simple computation of the nonlinear parameter functionals of the EDM. For small discretization intervals, the functionals can be linearized, and standard software permitting only linear parameter restrictions can be used. However, in this case the SEM approach must handle large matrices leading to degraded performance and possible numerical problems. The methods are compared using coupled linear random oscillators with time-varying parameters and irregular sampling times.
For Part 1 see [Zbl 1202.62124].

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
62M20 Inference from stochastic processes and prediction
65C30 Numerical solutions to stochastic differential and integral equations

Citations:

Zbl 1202.62124

Software:

LSDE
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Full Text: DOI

References:

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