In this paper we prove that, under suitable regularity assumptions, a necessary condition for the existence of a finite-dimensional filter in discrete time is the possibility of finding a convenient decomposition of the filter system s(z, y) into a sum of a term depending only on the first variable plus one depending only on the second one. We also give additional results concerning the observation, prediction and filtering distributions.
On Finite Dimensional Filtering In Discrete-time
FERRANTE, MARCO
1991
Abstract
In this paper we prove that, under suitable regularity assumptions, a necessary condition for the existence of a finite-dimensional filter in discrete time is the possibility of finding a convenient decomposition of the filter system s(z, y) into a sum of a term depending only on the first variable plus one depending only on the second one. We also give additional results concerning the observation, prediction and filtering distributions.
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