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Convergence in nonlinear filtering for stochastic delay systems. (English) Zbl 1152.60035

Summary: We study an approximation scheme for a nonlinear filtering problem when the state process \(X\) is the solution of a stochastic delay diffusion equation and the observation process is a noisy function of \(X(s)\) for \(s\in [t-\tau,t]\), where \(\tau\) is a constant. The approximating state is the piecewise linear Euler-Maruyama scheme, and the observation process is a noisy function of the approximating state. The rate of convergence of this scheme is computed.

MSC:

60G35 Signal detection and filtering (aspects of stochastic processes)
62M20 Inference from stochastic processes and prediction
93E10 Estimation and detection in stochastic control theory
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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