On the stochastic differential equations of filtering theory (Q5966360)

The author considers the filtering problem of optimally estimating the state process of a continuous-time nonlinear Itô type stochastic system from an incomplete nonlinear and noisy observation process. He thoroughly surveys the derivation and the connections of the related equations, i.e. the Fujisaki-Kallianpur-Kunita or Kushner equation, the Zakai equation, and Pardoux's bilinear stochastic partial differential equation which may be reduced to Clark's non-stochastic partial differential equation parametrized by the sample paths of the observation process. Robustness considerations with respect to modelling inaccuracies and hints on generalizations are given as well.