Some recent developments in nonlinear filtering theory
From two different points of view the authors review recent results in nonlinear filtering theory. The first part describes the use of (Itô-) stochastic calculus in estimating the state of a system from some observations, where the noise in both the signal and the observations is modeled by a Wiener process. Thus the authors derive the stochastic differential equation and the stochastic partial differential equation for the optimal filter. The second part is devoted to the finitely additive white noise model in filtering theory introduced by Balakrishnan. For this seemingly more practical and applicable model the analogous results are derived and compared to the filter equations for the Wiener model in part one. This comparison reveals a deep insight into connections between the recent attempts of making the Wiener-noise filtering model more instrumentable (Davis' robust solutions, Pardoux's solutions to s.p.d.e. etc.) and the finitely additive noise model.
scientific article; zbMATH DE number 3846578
scientific article