A generalization of the Kalman filter to models with infinite variance (Q689167)

The authors study a linear filtering system based on two càdlàg semimartingales. As stochastic integrals w.r.t. these semimartingales are well defined for bounded measurable deterministic functions, they consider a sort of \(L^ p\)-norms \((1<p \leq 2)\) in order to develop the framework of filtering theory for models with infinite variance. Recursive equations giving the optimal filter are established; they reduce to the classical Kalman-Bucy equations when the filtering system has independent white noises. Properties of the left innovation process are given. Therefore, formulae for the prediction and smoothing problems are obtained.