Wj. Runggaldier et F. Spizzichino, Sufficient conditions for finite dimensionality of filters in discrete time: a Laplace transform-based approach, BERNOULLI, 7(2), 2001, pp. 211-221
The discrete-time filtering problem can be seen as a dynamic generalization
of the classical Bayesian inference problem. For practical applications it
is important to identify filtering models that, analogously to the linear
Gaussian model (Kalman filter), admit a finite-dimensional filter or, equiv
alently, a finite-dimensional family of filter-conjugate distributions. Our
main purpose here is to give sufficient conditions for the existence of fi
nite-dimensional filters. We use a method, based on the Laplace transform,
which is also constructive.