Abstract
Before discussing the filtering problem, we prove a number of results in preparation for the martingale approach to the stochastic differential equation of the optimal filter which will be derived in the later sections of this chapter. Let us recall that (Ω,A,P) is a complete probability space and (ℱ t ) (t ∈ R + ) is an increasing family of sub σ-fields of A, and that it will be assumed that all P-null sets belong to ℱ0. The following processes are given on Ω: (S t ) called the signal or system process; (Z t ), the observation process; and (B t ), the noise process. All three are related by the model
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© 1980 Springer Science+Business Media New York
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Kallianpur, G. (1980). The General Filtering Problem and the Stochastic Equation of the Optimal Filter (Part I). In: Stochastic Filtering Theory. Stochastic Modelling and Applied Probability, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6592-2_8
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DOI: https://doi.org/10.1007/978-1-4757-6592-2_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2810-8
Online ISBN: 978-1-4757-6592-2
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