Abstract
This paper considers some bounds for the Hellinger distance in spaces of probability measures induced by partial observations of a stochastic evolution equation using some results of F. Liese [18], [19] and a technique developed in [15]. The basic aim of the reported work is to discover those perturbations of the infinite dimensional system generator that will lead to calculations of Hellinger balls. The main result here is an asymptotic localization property, in terms of the variation distance (see [25]), derived under some fairly restrictive assumptions on a perturbing operator as the observation interval increases to infinity. A prerequisite for this is a study of the perturbation properties of the covariance operator of the filtering error under stability and stationarity assumptions.
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© 1988 D. Reidel Publishing Company
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Koski, T. (1988). On Asymptotic Localization by Perturbing Operators for Partial Observation of a Stochastic Evolution Equation. In: Albeverio, S., Blanchard, P., Hazewinkel, M., Streit, L. (eds) Stochastic Processes in Physics and Engineering. Mathematics and Its Applications, vol 42. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2893-0_12
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DOI: https://doi.org/10.1007/978-94-009-2893-0_12
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