Abstract
In this paper we consider the filtering problem for the Hilbert space-valued stochastic process over discrete-continuous observations. The filtering equations are obtained for the optimal estimate ( conditional expectation ) and covariance operator in both integral and differential forms. A separate section is devoted to the case of discrete observations. For instance, the filtering problem for the heat equation is investigated.
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© 1993 Springer-Verlag
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Orlov, Y.V., Basin, M.V. (1993). On filtering of the hilbert space-valued stochastic process over discrete-continuous observations. In: Curtain, R.F., Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems. Lecture Notes in Control and Information Sciences, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0115034
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DOI: https://doi.org/10.1007/BFb0115034
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